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1. I Pseudotensors in different dimensions

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...

3. I Pseudotensors in different dimensions

May you explain way Paul Colby in theme https://www.physicsforums.com/threads/vectors-in-minkowski-space-and-parity.937349/ said me that
4. I Pseudotensors in different dimensions

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...
5. I Pseudotensors in different dimensions

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.
6. I Pseudotensors in different dimensions

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...
7. I Pseudotensors in different dimensions

May you explain why?
8. I Parity of theta term of Lagrangian

Thank you for replying. Would you say my reasoning above is true?
9. I Vectors in Minkowski space and 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...
10. I Pseudotensors in different dimensions

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. -...
11. I Parity of theta term of Lagrangian

it seems the topic is needed to shift in "High Energy, Nuclear, Particle Physics".
12. I Parity of theta term of Lagrangian

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...
13. Operation with tensor quantities in quantum field theory

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...
14. Quantum QFT: groups, effective action, fiber bundles, anomalies, EFT

Yes. Thank you for advice. Is there something other than Weinberg? And I would like to know are there any QFT books written from a mathematical view?
15. Quantum QFT: groups, effective action, fiber bundles, anomalies, EFT

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...
16. I Levi-Civita symbol in Minkowski Space

Do you understand what I'm saying?
17. Mathematica Part of complex plot disappears [mathematica]

I have a very large expression: j - Sqrt[q^2 + qp^2 - 2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 + 1/2 (16 m5^2 + ma^2 + mp^2 - Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0 where \[Theta] = Pi/6; ma = 980; mp = 139...
18. I Levi-Civita symbol in Minkowski Space

But is module from $$\epsilon_{0}^{\sigma\lambda\rho} q_{\sigma} p_{\lambda} e_{\nu}$$ just $$\epsilon_{0}^{\sigma\lambda\rho} q_{\sigma} p_{\lambda} e_{\nu}$$?
19. I Levi-Civita symbol in Minkowski Space

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.
20. I Levi-Civita symbol in Minkowski Space

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?
21. I Levi-Civita symbol in Minkowski Space

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?
22. I Levi-Civita symbol in Minkowski Space

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.
23. I Levi-Civita symbol in Minkowski Space

What about (3)-(5)? I think that it is incorrectly.
24. I Levi-Civita symbol in Minkowski Space

I set eyes on the next formulas: \begin{align} E_{\alpha \beta \gamma \delta} E_{\rho \sigma \mu \nu} &\equiv g_{\alpha \zeta} g_{\beta \eta} g_{\gamma \theta} g_{\delta \iota} \delta^{\zeta \eta \theta \iota}_{\rho \sigma \mu \nu} \\ E^{\alpha \beta \gamma \delta} E^{\rho \sigma...
25. Mathematica Numerical solution of integral equation with parameters

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...
26. A Software for symbolic calculations in high energy physics

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...