# Questions tagged [spinors]

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518 questions
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### Why two different spinors are Grassmann quantities?

In Rydberg Quantum Field Theory page 441 (this edition, unfortunately page 441 is not in the link) it says If $\xi$ and $\eta$ are Majorana spinors [...] and since $\xi$ and $\eta$ are Grassmann ...
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Trying to understand some about Lorentz invariance and representation theory, I thought that the best way is with an example of application: Show the Lorentz invariance of the Dirac Equation $$(i \... 0answers 103 views ### Physical/geometrical interpretations of spinors? Physically, a scalar is a quantity invariant with reference frame, a vector is a quantity associated with a direction, tensors are higher relationships between vectors - what are spinors? I thought I ... 0answers 39 views ### When I construct SUSY multiplet how can I distinguish a Majorana fermion from a Weyl one? When I construct a SUSY multiplet (massive or massless) I can act with the supercharges on a Clifford vacuum and construct the states in the multiplet, that I could interpret in terms of “ordinary” ... 0answers 27 views ### Can we say the origin of spin is due to mixing of various components of field under Lorentz transformation? when x,y,z,t are transformed under Lorentz transformation all the components get mixed up and gives the angular momentum conservation of the field. On the other hand if the field has some components ... 0answers 28 views ### Why is spinor along x-axis biased in terms of probability? If we use the Paulispin matrices of x-axis to find its Eigenvalues and eigenstates and use those to represent a spin state, we get the equation: when we look at spinor in terms of along x-axis, the ... 1answer 58 views ### Spin of an electron (What is the meaning of spinor in terms of Hilbert space and Euclidian space?) In quantum mechanics, electron has a spin of 1/2 either up or down. As shown by the Stern-Gerlach experiment, the spin is quantized so it could only be either up or down. The spinor matrices, for ... 0answers 71 views ### Some clarification on Dirac and Weyl spinor terminology I came across a seemingly trivial exercise in Schwartz's "QFT and the Standard Model" that I am just a little confused about. The problem is 11.6, "The physics of spin, helicity and chirality". (a) ... 1answer 86 views ### Why a 2-state photon is interpreted as spin 1? Both Ising spin and photon's polarization degree of freedom are used in quantum information as Qbit implementation. They both have 2 level state systems, which means mathematically their state could ... 2answers 258 views ### A simple question about the scattering amplitude \mathcal{M} in QFT Every scattering amplitude that I see have all the tensor indices contracted but spinor indices floating around, whose only disappear after you square the amplitude and do the sum and average over ... 2answers 357 views ### Choice of Dirac gamma matrix representation and definition of adjoint spinor Is the definition of the adjoint spinor \bar{\psi}=\psi^\dagger \gamma^0 forcing a particular choice of representation of the Dirac matrices (or a subset of the possible choices)? More precisely, I ... 1answer 161 views ### Dirac spinor parity I'm not sure I understand the effect of a parity transform on a Dirac spinor \left( \begin{array}{c} \psi_R\\ \psi_L\\ \end{array} \right). I've been given the definitions P\psi=\gamma_0\psi, ... 2answers 415 views ### spinor vs vector indices of Dirac gamma matrices I am struggling to understand the nature of the components of the Dirac matrices. If we view the four components of a Dirac spinor as \psi^a with a being a 'spinor' index, then if a gamma matrix ... 1answer 157 views ### What's the reasoning behind propagators definitions (specifically fermionic propagators) I'm studying QFT by David Tong's lecture notes. When he discusses causility with real scalar fields, he defines the propagator as$$D(x-y)=\left\langle0\right|\phi(x)\phi(y)\left|0\right\rangle=\int\...
I am having some basic questions about how to interpret Lagrangians, lets start with Dirac: $L = \bar{\Psi} (i \gamma^{\mu} \partial_{\mu} -m) \Psi$, where $\Psi$ is a Dirac-Spinor, $m$ is the mass,...