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  • Akarsh Simha 9:34 am on February 10, 2011 Permalink
    Tags: Physics, QFT   

    Why the i \epsilon? 

    Finally, I felt I had something about Physics that I wanted to write about. The i \epsilon terms sitting in the propagator of a QFT, in the Lippmann-Schwinger equation and in Chapter 4 of Peskin and Schroeder have been bothering a couple students including me at the department for a while now. I am not qualified enough in Quantum Field Theory to make any serious comments on this, but I just had some thoughts regarding the i \epsilon. They may be wrong, and I request readers to correct me if there are mistakes, or if they have something to add to this.

    At first look, the i \epsilon looked like some bizzare mathematical trick, put in by hand, to give meaning to integrals. “Oh, this integral diverges, but we want it to converge, so we just throw in an i \epsilon”. A lot of us were pretty dissatisfied with this. Also, there was this question too — there are these i \epsilon terms in (a) the propagator, (b) in the Lippmann-Schwinger equation, (c) in Peskin-Schroeder’s derivation relating the interacting ground state with the free-theory ground state, and (d) in the derivation of the path integral formalism from canonical QM — are they all stuck there for the same purpose?

    The first time i \epsilon bothered us was in Peskin-Schroeder’s derivation of a relation between the free-field ground state and the interacting-field ground state, where he says “let us take time to infinity in a slightly imaginary direction”. Now, the question was, why should time become imaginary? A long argument on VoIP with Naveen Sharma was adjourned with this: “The T \to \infty( 1 + i \epsilon) is a mathematical trick to supress the contribution of all other states and solve for the interacting ground state in terms of the free-field ground state.”

    Then came Prof. Weinberg’s notes on the Lippmann-Schwinger equation. As he explained in class, and as was explained in his notes, the right choice of ± i \epsilon in the Lippmann-Schwinger Green’s function fixes whether we are choosing in-states or out-states. i.e. states with the +i \epsilon in the Green’s function’s denominator satisfy the condition that they look like free particles in the asymptotic past, while states with the -i \epsilon look like free particles in the asymptotic future. A similar argument, with a bit more detail, is presented in his book “The Quantum Theory of Fields” volume 1, in Chapter 3. He also has made a reference to B. A. Lippmann and J. Schwinger, Phys. Rev. Vol 79, No. 3 (1950)..

    So I briefly looked at the Lippmann-Schwinger paper, where they actually derive the equation. Then they make a comment: “simulating the cessation of interaction, arising from the separation of component parts of the system, by an adiabatic decrease in the interaction strength as t → ± \infty. The latter can be represented by a factor exp(-\epsilon |t|/ħ) where \epsilon is arbitrarily small.” Aha! So that epsilon came from an adiabatic (slow) decrease of interaction strength! But why are we forced to kill that interaction “by hand”? [PS: Loophole — I still don’t know the adiabatic theorem] I don’t know enough, but I’d ordinarily expect a “factor killing the interaction” to sit in the interaction Hamiltonian rather than outside it (see eqn 1.51 of the Lippmann-Schwinger paper).

    At least now, the \epsilon factor had some physical meaning — it came from the adiabatic killing of the interaction, rather than being just some “pole-pushing technology”.

    More came today. There is the same epsilon in the Fourier transform of a \theta function (Heaviside step function). One may write:

    This is something that I was supposed to know from Electrical Engineering, but we used to “throw away” the epsilon — it didn’t matter much there I guess. Really, it’s just the Fourier transform of a decaying exponential (which every electrical engineer, from IIT Madras at least, would know) with the characteristic length taken to infinity. And then, today we worked out the Feynman propagator for the scalar field. I should’ve known this long back, but I learned it today, that really, the epsilon in the propagator comes from the \theta function’s Fourier transform.

    So it seems like the epsilons — at least in (a), (b) and (c) — are present to impose causality.

    And then, I learned something more today: An i\epsilon is going to make the Hamiltonian non-Hermitian (eg: See the Green’s function in the Lippmann-Schwinger: it’s effectively adding a small non-Hermitian component to the Hamiltonian). And we see that Hermiticity of the Hamiltonian is required for time-reversal symmetry:

    Thus, if my logic is right, the i \epsilon is necessary to break the time-reversal-invariance in the system so that we can talk about an “in” state and distinguish that from an “out” state. Of course, this is unphysical in most situations as far as we know, so we do away with the \epsilon at the end.

    Now, this brings me to a couple of questions:

    • Does that mean the weak interaction has a non-Hermitian Lagrangian density? [Need to check; sounds like a No]
    • We’re always time ordering in quantum mechanics. A naïve look gives me the impression that time ordering breaks time-reversal invariance. Then why are our theories time-invariant?

    Anyway, so much for an epsilon!

    • Janakiraman 12:56 am on March 18, 2011 Permalink | Log in to Reply

      Couple of suggestions. I think of the i\epsilon in the propogator as something that results due to the laplace transform of the propogator. You cannot take a fourier transform it is not absolutely integrable no matter what. Another the hamiltonian needs to be hermitian no matter what, since your energy eigen values can’t be complex. The time reversal symmetry is true if your Hamiltonian is real. This is why this property is lost when we have the vector potential corresponding to the B field (though the Hamiltonian is hermitian).

  • Akarsh Simha 2:24 am on April 20, 2009 Permalink
    Tags: career, Dual Degree, education, , , , JEE, Masters, Physics   

    For IIT aspirants wanting to pursue Physics 

    The Physics Department, IIT Madras is offering an Dual Degree MS programme in Physics!

    The Course:

    The course is a 5 year Dual Degree MS programme. The first two semesters of the course will be common with the rest of the engineering branches, excepting some variations where engineering-oriented courses will be replaced by more fundamental courses. This is designed so that branch-change after the end of the first semester is possible. At the end of the 5 years, (as is the case with any other dual degree programme), the student will be given both a Bachelor’s degree and a Masters’ degree in Physics. Entrance will be through the Joint Entrance Examination (JEE).

    The intake per year stands at 10 students.

    Worthy of mention is an innovative course on ‘Contemporary Physics’ – named so (as Prof. V Balakrishnan put it) because ‘Modern Physics’ still refers typically to de Broglie’s hypothesis! This course will focus on the latest advances in various branches in Physics and will be taught by several faculty from the department.

    The Department:

    The Department of Physics at IIT Madras is, in my opinion, probably one of the best Physics departments that you’d get across the country in the IITs.

    The department has a strong low temperature and condensed matter group, a strong atomic and molecular physics group, a strong optics group, and a strong theory group working in fields like Quantum Information, String Theory, Dynamical Systems and Statistical Physics. Worthy of mention is the nanosciences group, out of which several patent-winning innovations have sprung up. An astrophysics group is expected to form very soon.

    At the undergraduate level, in addition to the 5-year Dual Degree MS programme, the department offers a 4 year B.Tech. programme in Engineering Physics.

    Physics has grown far from what we studied at JEE. Here are some of the stuff that’s done at the department:

    Personal Opinions

    I’m a student in the Engineering Physics [EP] BTech programme in this department and have an inclination towards Theoretical Physics. I find the courses in the department very enjoyable and find most of the faculty outstanding. Most faculty are very helpful and warm, and try to do their best to ensure you a successful career.

    I also find the subject matter of theoretical physics very enjoyable. We’ve been doing a lot of “fun” stuff (far more fun than JEE physics) like studying the chaotic dyanmics of population growth, solving for the curvature of spacetime around a blackhole, describing interactions of LASER light with an atom quantum, studying functions with very weird singularities, or working dynamics in some “twisted” spaces in our courses so far! As Feynamn points out, there’s something called ‘Intellectual Enjoyment’ and classes in the last 2 years have been an experience of the same.

    That apart, we also have a theory discussion group called ‘Boltzmann’ out here which meets on Saturdays in the department. We discuss theory just for fun. We discuss rather advanced topics in various branches of Physics. We discussed the ‘Ising model’ last semester, and one of my batchmates took that forth into a model for economic markets that he’s currently working on. This semester, we discussed a wide variety of topics including Quantum Information Theory, Quantum Computing, Group Theory and some quantizations of fields.

    I guess the MS programme will be just as much fun (or maybe even more – hey, you don’t do some boring old courses on Fourier transforms!) as the EP programme. If you have a strong liking for Physics, then the Dual Degree MS is probably for you. If you’re still ‘undecided’, the Engineering Physics programme may be a good idea as it gives you the required credentials to continue as an Electrical Engineer.


    If you need some help deciding, you could contact me < akarshsimha AT gmail DOT com >; my friend from EP, Naveen < naveensharma30 AT gmail DOT com >; or Dr. Suresh Govindarajan < suresh AT physics DOT iitm DOT ac DOT in >. All of us will be happy to help you make a decision or tell you what Physics is like!

    For those of you curious, I’m now at the University of Texas at Austin, Austin, TX, USA, and am pursuing a PhD in physics. My work is currently a mix of experimental physics and theory.

    • Srinidhi 9:12 pm on April 19, 2009 Permalink | Log in to Reply

      Popularizing Physics 🙂 Way to go. MS program in physics really sounds good. I felt 4 years is too less to learn much. This will surely turn out to be a good experience.

    • SG 8:26 am on May 28, 2009 Permalink | Log in to Reply

      Is there any way to get the info on this page through to students who have passed JEE?

    • Akarsh Simha 12:20 pm on May 28, 2009 Permalink | Log in to Reply

      @SG: By that, do you mean some sort of mailing list? I wonder if there is. Orkut communities and Facebook groups may be a good way to do that. There could be other forums too. I guess Naveen uses one of Orkut / Facebook, and I’ll request him to post this stuff out there.

      But I’m getting quite a few emails from interested folks these days.

    • SG 5:11 pm on May 28, 2009 Permalink | Log in to Reply

      Yes that is what I meant. It is good to hear that you are getting emails — I haven’t got any.

    • Manu 12:00 pm on May 29, 2009 Permalink | Log in to Reply

      Hello, I got AIR 3000 in JEE 2009, is there any chance that I’ll get into this course? please reply…and should I join IIT-K if I get into the 5 yr. MSc. physics course?

    • Akarsh Simha 12:43 pm on May 29, 2009 Permalink | Log in to Reply

      Hi Manu. I can’t predict very well because the course is new, but I’d say there’s some chance of getting it.

      Again, it depends on what you want to do. As far as I know, the IITK Physics Department is stronger in Experiment and IITM Physics Dept. is stronger in Theory. But you should probably ask an IITK MSc Physics student for his views.

    • Thirunanasambandar 7:24 pm on June 1, 2009 Permalink | Log in to Reply

      IIT Madras is a dud place in the Sciences, always was. Go there at your own peril. Who have they produced with a serious reputation in either Physics or Mathematics. They know nothing about Calabi’s conjectures or Yau’s work and BS about it.
      Better they close the deptt. and send the professors to farm fields.

    • Akarsh Simha 11:05 am on June 2, 2009 Permalink | Log in to Reply

      I hear that the Physics Dept. at IITM was relatively bad about 20 years back. But that’s no longer the case – we have some well known physicists as faculty at our department. Of course there is no peril in the present day. After all, I’m a student there now, so I can vouch for that.

      It is not true that IITM physics graduates have not done well. For instance, the 2009 Lars Onsager Prize winner is from IITM and there are many more.

      On a side note, there’s no reason for Physics faculty to know algebraic geometry.

    • Anurag 1:35 am on June 10, 2009 Permalink | Log in to Reply

      I have qualified the JEE this year and I aspire to become a theoretical quantum- or maybe astro- physicist. I think my rank can get me the integrated msc physics course at IIT Kanpur. But after reading your blog i am very curious about the courses : BS,MS dual degree at IITM and Engineering Physics. Can you please explain the difference between the three courses?
      If I opt for Engineering Physics now can I later become a Quantum Physicist or an Astrophysicist?
      It will be very helpful of you if you could answer my question before 13th June.

    • SG 2:26 pm on June 10, 2009 Permalink | Log in to Reply

      Hi Anurag,

      The course at IITK is called the integrated M.Sc. program in Physics and offers a M.Sc. degree at the end of five years. The new course at IITM gives two degrees (BS and MS) at the end of two years. Otherwise both are five year programs in Physics. At IITM, it is envisaged that the fifth year will be spent on working on a research project and doing advanced electives in the area of one’s interest. This is different in approach from a conventional M.Sc. program.

      The Engineering Physics (EP) program at IITM has its core curriculum equally split between EE and Physics. About a third of the students pursue higher studies in Physics, another third in EE and the final third go for jobs/MBA etc.
      So it is possible to study any area on physics — theoretical as well experimental after obtaining a degree in EP. However, the five year programs are much more tailored to pursuing a career in physics while the EP program keeps open the option of pursuing Electrical Engineering.

      Best of luck.

      • SG 3:15 pm on June 10, 2009 Permalink | Log in to Reply

        There is a typo in what I wrote — I wrote “end of two years” when I meant “end of five years” in the first paragraph.

    • SG 8:55 am on June 14, 2009 Permalink | Log in to Reply

      I am posting a relevant email exchange.

      > Respected Sir,
      > I am interested in the new course Physics dept. at IITM is
      > providing (B.S + M.S in Physics). How is this course different
      > from Engineering Physics and what is the Curriculum? How will
      > the research opportunities for this course be? Is this M.S
      > degree in any way different from the M.S degree provided by
      > most American universities? Thank you very much for your
      > valuable time.
      > Yours sincerely,
      > Vijay Varma

      Thank you for your email. I believe the new 5-year Dual Degree MS in
      Physics that will be offered by IIT Madras from July 2009 will be a
      rigorous and thorough course in physics, with several new components that
      will make it both instructive and interesting. Numerous elective courses
      will be offered, which will enable a student to choose his/her stream
      according to interest and aptitude, both theoretical and experimental. The
      final year will have a serious project component, and it is hoped that the
      project work will lead up to a research paper in most cases. The BTech in
      Engg Physics is a 4-year course, and has a significant electrical
      engg/electronics component. It is also an excellent course. I can’t say
      precisely how our MS course will differ from the MS in most US
      universities, because the latter varies widely from one university to
      another, and is also based essentially on course work alone. (Of course
      the BS in those universities requires a senior thesis in the 4th year.) We
      envisage our MS course to be such that a student can essentially start
      research work right after graduation—in a typical US university, our
      students should be able to take the qualifiers for the PhD within a
      semster of getting there, without having to take many of the standard
      first year graduate courses. But of course this depends on the level of
      preparedness of the student, espcially with regard to problem-solving. It
      is very probable that the core courses at IIT Madras in subjects such as
      Classical Mech., Quantum Mech., EM Theory, Stat. Mech., Math. Phys. will
      provide adequate preparation in this regard, if a student takes the
      problem sets and assignments seriously. I might also point out that a very
      good choice for students whose academic performance in the MS course is
      good would be to enrol for research at IIT Madras itself, as the
      Department has a vibrant and wide-ranging programme of research in a wide
      variety of areas.

      Best wishes,

      V. Balakrishnan

    • SG 9:09 am on June 14, 2009 Permalink | Log in to Reply

      During the first couple of days of counselling, I noticed a common misconception about pursuing a 5 year programme in Physics. Invariably, people assume that the ONLY option on graduation is to pursue higher studies followed by a career in academia.

      My guess is that this route will be followed by around a third to half of the students. What about the remaining students? I anticipate that they can find jobs in industry — there is a large gray area connecting physics and engineering. I can see a company working in solar cells hiring a M.S. (Physics) student, a similar thing would hold for a company doing work in semiconductor devices, nanotechnology etc. Of course, software jobs will continue to take in a percentage of such graduates.

    • Souvik 11:12 pm on June 30, 2009 Permalink | Log in to Reply

      Hello Sir,
      I had an interest in Physics which strengthened in the preparatory years for IIT-JEE. I had opted for EP in IITB and have got the same. Initially, I had felt that I had made the right decision, but now I feel that it was quite a risky thing to do. Could you please explain the future prospects for it, incase that I’m able to go to some coll in the Ivy League in the US.

    • SG 5:13 pm on July 2, 2009 Permalink | Log in to Reply

      Here was my response via email to Souvik

      Dear Souvik,

      EP at IIT Bombay is a very good program. I know of several people who have graduated from that program who have gone on to study at Princeton, Cornell and such top universities in both Physics and Electrical Engineering.

      Please go and spend the next four years learning and adding value to yourself. Then, the sky is the limit.

      With best wishes,

    • sri ram 1:37 pm on February 28, 2010 Permalink | Log in to Reply

      sir, could you explain the difference between integrated msc physics in iit kharagpur and dual degree ms physics in iit madras.I am interested in working as professor in physics .

    • Akarsh Simha 4:12 pm on February 28, 2010 Permalink | Log in to Reply

      Hi Sriram, please look at the reply by “SG” to Anurag. The same applies to IIT Kharagpur as well.

    • TANOY 4:13 pm on April 5, 2010 Permalink | Log in to Reply

      I am a iit aspirant..i am interested in physics.i want to do a physics course in iit.but little bit confused about the course engineering physics ,ms&ds dual degree in physics&integrated msc physics.please help.

    • Dhruv Sharma 12:10 am on May 19, 2010 Permalink | Log in to Reply

      hello sir thank you so much for actually putting up this information. i was beginning to think that i might be the only person to be interested in 5yr physics course.
      but my bigger query is that whether the curriculum is so desigened so that i can pursue mathematical physics in the future(that is my aim so as to say). also will the 5yr degree be a hindrance to pursue advanced PhD programmes abroad as in the US beacuse i presume that the requirements are rather different.
      Please do make the effort to answer my query as it will really help me to take a firm decision. because up until this point i am confused between Math and Physics and on the bigger issue of what best suits me and will make a good career path,

    • AMIR 12:58 am on June 29, 2010 Permalink | Log in to Reply

      i got seat in 5 year BS and MS dual degree in physics in IIT MADRAS.
      sir please tell me about the scope and past year records of this stream in terms of placement through campus…

    • Lokesh Mishra 1:17 am on April 13, 2011 Permalink | Log in to Reply

      ok akarsh nice post……..nice to c guyz wid mutually gud feelings for physics……. i have given thee jee-2011, bound to clear it
      but i am in a dilemna:
      isnt it true dt deir r less job opportunites for b. tech. in EP.
      althogh m cocenterating hard on”enjoying the study” part… but it doesnt skip my mind, dt other branches offer not just many jobs but also higher packages……..
      so dude
      i xpect u to end my “toe-bitting CONFUSION”

      waiting sincerely for ur reply

    • VBM 6:57 pm on April 21, 2011 Permalink | Log in to Reply

      That is not really true. EP graduates from the institute in the past have landed up great jobs on par with their counterparts in other departments. Apart from the avenues in physics like grad school and then research etc that will open up to you after four years the course is unique in that you also can jump into electrical engineering due to the many courses in the EE department that are part of the curriculum. Of course jobs in other unrelated fields too have vowed many of previous aluimni since they look for soft skills etc that are not department specific.

    • Rahul Nair 9:01 pm on April 26, 2011 Permalink | Log in to Reply

      i am about to write jam 2011 and continue research in particle physics,quantum theories etc.where shuould i join for msc as am confident enough to clear jam 2011

    • kstar 8:34 am on April 27, 2011 Permalink | Log in to Reply

      Hi Lokesh, Dhruv, Amir, and Rahul,

      I’ll be happy if you could mail me your questions as using this comment thing to reply is rather cumbersome and I can’t answer point-by-point like I can on email.

      My email address is akarshsimha AT gmail DOT com.

    • nishant jain 8:53 pm on June 3, 2011 Permalink | Log in to Reply

      which is better engg phy or m.sc phy?
      pls reply soon.

    • DG 6:51 pm on June 5, 2011 Permalink | Log in to Reply

      I got an AIR 895 for JEE this year and I have yet to decide what course I should opt for. I’m interested in theoretical physics. I am currently considering the EP programme and the dual degree B.S. and M.S. Physics programme. I hear that the EP programme is better to get good placements and salaries but it is focused mainly on electrical enigneering which I am not a fan of. The dual degree programme’s syllabus sounds more interesting but i’m not sure whether there is much scope for jobs apart from research in this field. I would like to know which course would be better for good jobs and would be more interesting. Also I want to know whether to go to IIT madras or IIT bombay.

    • aniket 12:46 pm on June 10, 2011 Permalink | Log in to Reply

      should i go for engineering physics in guwahati?

    • Suhas 11:36 pm on June 12, 2011 Permalink | Log in to Reply

      Is there any scope for jobs in india for Msc or BS MS physics course from iits apart from research and management line? Please do reply soon

    • Suhas 11:42 pm on June 12, 2011 Permalink | Log in to Reply

      Is there any scope for jobs in india for Msc or BS MS physics course from iits apart from research and management line? Please do reply soon…..

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