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    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...
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    I Vectors in Minkowski space and parity

    Please see continuation of my questions in this thread https://www.physicsforums.com/threads/pseudotensors-in-different-dimensions.937348/#post-5924496
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    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
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    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...
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    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.
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    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...
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    I Parity of theta term of Lagrangian

    Thank you for replying. Would you say my reasoning above is true?
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    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...
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    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. -...
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    I Parity of theta term of Lagrangian

    it seems the topic is needed to shift in "High Energy, Nuclear, Particle Physics".
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    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...
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    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...
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    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?
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    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...
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    I Levi-Civita symbol in Minkowski Space

    Do you understand what I'm saying?
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    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...
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    I Levi-Civita symbol in Minkowski Space

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

    What about (3)-(5)? I think that it is incorrectly.
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    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...
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    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...
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    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...
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