Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    2
    ReputationRep:
    I'm a little confused by the explanation on this in my textbook.

    For a variation in just the field we have  \delta \phi(x) = \phi' (x) - \phi(x)

    For a variation in the field and the argument we have
     \delta_T \phi(x') = \phi'(x') - \phi(x) = \delta \phi(x') + \frac{\partial \phi}{\partial x_{\beta}}\delta x_{\beta} =  \delta \phi(x) + \frac{\partial \phi}{\partial x_{\beta}}\delta x_{\beta}
    where in the last step only first order terms in small quantities have been kept. I don't understand why x' becomes x when only considering first order in small quantities.

    There's then a line that claims that  \mathcal{L} (\phi'(x'), \phi,_{\alpha}(x')) - \mathcal{L} (\phi(x), \phi,_{\alpha}(x)) = \delta\mathcal{L} + \frac{\partial \mathcal{L}}{\partial x^{\alpha}}\delta x^{\alpha} . I have no idea where this comes from.
    Offline

    0
    ReputationRep:
    (Original post by suneilr)
    I'm a little confused by the explanation on this in my textbook.

    For a variation in just the field we have  \delta \phi(x) = \phi' (x) - \phi(x)

    For a variation in the field and the argument we have
     \delta_T \phi(x') = \phi'(x') - \phi(x) = \delta \phi(x') + \frac{\partial \phi}{\partial x_{\beta}}\delta x_{\beta} =  \delta \phi(x) + \frac{\partial \phi}{\partial x_{\beta}}\delta x_{\beta}
    where in the last step only first order terms in small quantities have been kept. I don't understand why x' becomes x when only considering first order in small quantities.

    There's then a line that claims that  \mathcal{L} (\phi'(x'), \phi,_{\alpha}(x')) - \mathcal{L} (\phi(x), \phi,_{\alpha}(x)) = \delta\mathcal{L} + \frac{\partial \mathcal{L}}{\partial x^{\alpha}}\delta x^{\alpha} . I have no idea where this comes from.
    Try thinking in terms of a taylor expansion of the lagrangian to linear order.
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
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

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

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