# Search results

1. ### 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...
2. ### 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. -...
3. ### 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...
4. ### 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...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...