Questions tagged [dirac-matrices]

The tag has no usage guidance.

242 questions
Filter by
Sorted by
Tagged with
318 views

Diffeomorphisms and the Dirac action

I have a question concerning fermions in curved space-time. Please read it to the end before suggesting the spin-connection and vierbein-based approach. I heard that there is a special way of ...
130 views

Dirac matrices in 1+1 dimensions

Given $\gamma^\mu$ in 1+3 dimensions with signature $(+,-,-,-)$, how can I obtain Dirac matrices in 1+1 dimensions expressed in terms of the $\gamma^\mu$?
29 views

Evaluating a trace with two factors of $\gamma^5$

In the process of calculating a spin-averaged square amplitude in QFT, I came across the following expression: $$\text{Tr}\left[\gamma^\mu\gamma^5\gamma^\alpha\gamma^\nu\gamma^5\gamma^\beta\right]$$ ...
2k views

Fierz identity with Weyl spinors

The following Fierz relation does not seem so obvious to me: \begin{equation} \bar{\psi}_1 \gamma^\mu (1+\gamma_5)\psi_2 \bar{\psi}_3 \gamma_\mu (1-\gamma_5) \psi_4 = -2 \bar{\psi}_1 (1-\gamma_5) \...
180 views

Gamma matrices in (2+1)

I am sure that is very well-known question and see on this site several similar questions but I would like to specify the answer 1) I know that in $(2+1)$-dimensions one can construct $\gamma$-...
50 views

Confusion with trace of gamma matrices

Using $\{\gamma^\mu, \gamma^\nu\} = 2 \eta^{\mu\nu} \mathbf{1}$, it is easy to show that: \begin{align*} \operatorname{tr} \gamma^\mu \gamma^\nu = 4\eta^{\mu\nu} \end{align*} Now, it is also true that ...
2k views

66 views

Geometrized Algebra and Einstein's Equations

The algebraic properties of the pseudoscalar $i$ follows the ordinary rules for imaginary numbers: So its algebraic properties are ~ $i^2 = -1$ the amazing geometric property is that it is an ...
138 views

C and T Symmetry of Free Dirac Lagrangian

I want to show the $C$ and $T$ symmetry of the free Dirac Lagrangian $$\mathcal{L}=\overline{\psi}\left(i\gamma^\mu\partial_\mu-m\right)\psi.$$ Following the notation of Peskin, Schroeder, we have ...
66 views

Motivating the Unintuitive Properties of Spinors

In the usual treatment of (Dirac) spinors, one usually starts with "factoring" the energy-momentum relation, deducing the properties of the $\gamma$ matrices by requiring the cross terms to cancel, ...
24 views

Zero momentum in Non relativistic Quantum Mechanics and about Dirac matrices

In relativistic quantum mechanics, we can solve the Dirac's equation with an added condition that the momentum of the particle is $0$. However, such independence isn't provided by the Schrodinger's ...
117 views

Dimension of gamma matrices in dimensional regularization

When performing loop integrals in theories containing Dirac fermions, one almost always confronts terms of the form $$\text{Tr}\left[\gamma^{\mu_1}\cdots\gamma^{\mu_n}\right].$$ For instance, in $d$ ...
133 views

What is the transpose of Lorentz transformation under spinor representation?

Let $S$ be the Lorentz transfortmation under spinor representation, and from any quantum field theory textbooks, we know that $$S^\dagger=\gamma^0S^{-1}\gamma^0 \\ S^{-1}=\gamma^0S^\dagger\gamma^0$$ ...
181 views

55 views

73 views

A question about the decoupling of Dirac equation in 1+1 dimension

It is said that in 1+1 dimension, if we take $\gamma^0=i\sigma^2$ and $\gamma^1=\sigma^1$, then the two components of dirac spinor $\psi_L$(upper component) and $\psi_R$(lower component) decouple in ...
48 views

Mapping from spinor to tetrad

I am reading the journel by Patrick l. Nash: mapping from tetrad to Dirac spinor. While reading this ,I came across the term concrete real 4*4 irreducible representation of SO(3,3). I know SO(3) is ...
87 views

weak interaction are not parity invariant

I'm having some hard time trying to see why the left-handed lagrangian for fermions $\psi$, $$\mathcal{L} := G\overline{\psi}_{1L}\gamma^\mu\psi_{2L}\overline{\psi}_{3L}\gamma_\mu\psi_{4L}$$ is not ...
298 views

How to prove $\{\gamma^{\mu}, \gamma^{\nu}\}$ ? (notation problem)

I want to prove that $\{\gamma^{\mu}, \gamma^{\nu} \}=2g^{\mu \nu}$ what are the indices $\mu$ and $\nu$ here? because I know the gamma matrices from 0 to 5 and I need to verify the anti ...
43 views

Question about $\gamma^{0}$ matrix

I see different definitions in different places so here is my question. why is $\gamma^{0}$ sometimes defined as a 2 by 2 matrix and sometimes as a 4 by 4 matrix? shouldn't a definition be something ...
The 4D SUSY algebra can be written as $$\{ Q_{\alpha}^{A} , Q_{\beta}^{B \dagger} \} = 2 m \delta^{AB} \delta_{\alpha \beta} + 2 i Z^{AB} \Gamma^0_{\alpha \beta}, \tag{B.2.37}$$ in a particular ...