When I created themes I thought that it will be different topics. I wish to emerge themes but I cannot do it. I left the message in that thread because I thought that Paul Colby will be interested in this thread too but I apparently understand you not right... I'm sorry! I thought that you said...
Please see continuation of my questions in this thread https://www.physicsforums.com/threads/pseudotensors-in-different-dimensions.937348/#post-5924496
May you explain why happens such things. I thought that ##V^μ \rightarrow V^μ## if ##V^μ## is a 4-vector and ##W^μ \rightarrow -W^μ## if ##W^μ## pseudo-4-vector
I caught your statement about pseudo-tensors have to change their sign in odd dimension, but you nothing said about how it is...
Are you state that tensor Levi-Civita isn't pseudo-tensor?
May you advise literature where is a discussion about the difference between even-dimensional and odd-dimensional pseudo-tensor and how it links with parity? Because I did't get that.
For example vector of magnetic field is pseudo-vector and it is determined in three-dimension, isn't it?
Sorry, I don't quite understand your first message.
For example in this book http://farside.ph.utexas.edu/teaching/em/lectures/node120.html , author works in Minkovski space and uses parity...
It is known that vectors change them sing under the influence of parity when ##(x,z,y)## change into ##(-x,-z,-y)##
$$P: y_{i} \rightarrow -y_{i}$$
where ##i=1,2,3##
But what about vectors in Minkowski space? Is it true that
$$P: y_{\mu} \rightarrow -y_{\mu}$$
where ##\mu=0,1,2,3##.
If yes how...
In this topic https://physics.stackexchange.com/questions/129417/what-is-pseudo-tensor one answer was the next:
The action of parity on a tensor or pseudotensor depends on the number of indices it has (i.e. its tensor rank):
- Tensors of odd rank (e.g. vectors) reverse sign under parity.
-...
I have a very simple question. Let's consider the theta term of Lagrangian:
$$L = \theta \frac{g^2}{32 \pi^2} G_{\mu \nu}^a \tilde{G}^{a, \mu \nu}$$
Investigate parity of this term:
$$P(G_{\mu \nu}^a)=+G_{\mu \nu}^a$$
$$P( \tilde{G}^{a, \mu \nu} ) =-G_{\mu \nu}^a$$
It is obvious. But what about...
I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera.
I...
Hi, I am looking for textbooks in QFT. I studied QFT using Peskin And Schroeder + two year master's degree QFT programme.
I want to know about the next items:
1) Lorentz group and Lie group (precise adjectives, group representation and connection between fields and spins from the standpoint of...
But is module from $$ \epsilon_{0}^{\sigma\lambda\rho} q_{\sigma} p_{\lambda} e_{\nu}$$ just $$ \epsilon_{0}^{\sigma\lambda\rho} q_{\sigma} p_{\lambda} e_{\nu}$$?
No, my amplitude is $$ \epsilon_{0}^{\sigma\lambda\rho} q_{\sigma} p_{\lambda} e_{\nu}$$ where $$e_{\rho} e_{\alpha}=g_{\rho,\alpha}$$ and my model is effective Wess-Zumino-Witten action.
My square of the amplitude is $$ \epsilon_{0}^{\sigma\lambda\rho} \epsilon_{0}^{\mu\nu\alpha}g_{\rho\alpha}p_{\sigma}q_{\lambda}p_{\mu}q_{\nu}$$ and its sign depends of defenation (5) or (8). Don't I understand something?
Yes, for an amplitude an overall sign doesn't matter but my an amplitude is proportional Levi-Civita tensor and its square proportional Levi-Civita tensor on Levi-Civita tensor. Or for square of the amplitude does overall sign not matter too?
Thank you for answer, but what about (3)-(5)?. My question appeared from a fact that if I use (5) than I come to a negative square of an amplitude. And if I use (8) than square of an amplitude is positive one.
Hello! Could you tell me about how to take the next numerical calculation in mathematica? (perhaps there are special packages).
I have an expression (in reality slightly more complex):
## V=x^2 + \int_a^b x \sqrt{x^2-m^2} \left(\text Log \left(e^{-\left(\beta...
I interest the software, which understands gamma and sigma matrices, that the convolution can go over Lorentz indexs, and over group indexs, which understands what is covariant differentiation, trace.
I tried to use maple, but work goes with difficulty. Although I write convolution over...