Hey there! Sign in to join this conversationNew here? Join for free

Quantum theory , variation of S is zero, integrate by parts Watch

    • Thread Starter
    Offline

    3
    ReputationRep:
    Name:  qft variaton of s.png
Views: 10
Size:  18.3 KB1. The problem statement, all variables and given/known data

    Hi, Please see attached.

    I am trying to show the second equality , expressing all as a total derivative (I can then show that \delta S = )

    2. Relevant equations
    See above

    3. The attempt at a solution

    So the  m term is pretty obvious, simply using the chain rule. It is the first term I am stuck on.

    So looking by the sign, it looks like we have done integration by parts twice.

    My working so far is to go by parts initially as:

    w=\partial^{u}\phi
    \partial w = \partial_{v}\partial^{u} \phi
     \partial z =  \partial_{u}\partial_{v} \phi
     z= \partial_{u} \phi

    to get, since we are allowed to assume vanishing of the field \phi at inifnity:

     - \int \partial_{u} \phi ( \partial_{v} \partial^{u} \phi )

    I am now stuck of what to do, I can't see a move that will get the desired expression for a choice of integration by parts, which makes me question whether this was the correct first move to make.

    Many thanks in advance.
    Offline

    11
    ReputationRep:
    (Original post by xfootiecrazeesarax)
    Name:  qft variaton of s.png
Views: 10
Size:  18.3 KB1. The problem statement, all variables and given/known data
    I had a go at this, but got horribly lost in a sea of co- and contra- four-gradients. You could try posting either on physicsforums.com or physics,stackexchange.com, where there will certainly be people more able to help with this.

    The layout and presentation of your problem and working is very nice and clear, BTW.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    What newspaper do you read/prefer?
    Useful resources

    Make your revision easier

    Maths

    Maths Forum posting guidelines

    Not sure where to post? Read the updated guidelines here

    Equations

    How to use LaTex

    Writing equations the easy way

    Student revising

    Study habits of A* students

    Top tips from students who have already aced their exams

    Study Planner

    Create your own Study Planner

    Never miss a deadline again

    Polling station sign

    Thinking about a maths degree?

    Chat with other maths applicants

    Can you help? Study help unanswered threads

    Groups associated with this forum:

    View associated groups
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.