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Is it possible to construct an adjoint representation for the Lorentz group?

Why is it said that the cut-off regularization is not a Lorentz invariant regularization method?

In non-relativistic quantum mechanics, causality is violated by saying that the amplitude of propagation of a particle $$A=\langle \textbf{x}|\exp{\Big(\frac{-i\textbf{p}^2t}{2m\hslash}}\Big)|\textbf{ …

Suppose an inertial frame $S^\prime$ is moving with a relative velocity $\textbf{v}=v\hat{n}$ w.r.t another intertial frame S with their axes parallel and $\hat{n}$ is an arbitrary direction. In that …

The situation is completely symmetric. Let the velocity of a frame A w.r.t another frame B is $\textbf{v}$. then from the perspective of A, the frame frame B has a relative velocity $-\textbf{v}$. Fro …

In the metric convention $(+,-,-,-)$, the spacetime interval is given by $$x^2=x_\mu x^\mu=(x^0)^2-|\textbf{x}|^2=t^2-|\textbf{x}|^2$$ in the units $c=1$. To make the theory Euclidean one considers th …

In field theory, each elementary particle is associated with a field of its own. One writes down a Lagrangian (density) $\mathscr{L}$ for the field. When you quantize the theory you obtain particles. …

The conventional books on thermodynamics that I know, do not talk about the thermodynamics of relativistic systems. But in Cosmology, the thermodynamic concepts are often applied to the whole universe …

In Peskin and Schroder's Quantum field theory text (page 28, the passage below Eq. 2.53), it asserts that for a spacelike interval $(x-y)^2<0$, one can perform a Lorentz transformation taking $(x-y)\r …

The commutator of two free scalar fields at two spacetime points $x$ and $y$ given by $$[\phi(x),\phi(y)]=\int\frac{d^3p}{(2\pi)^32E_{\textbf{p}}}[e^{-ip\cdot (x-y)}-e^{ip\cdot (x-y)}]$$ is Lorentz-in …

If $\Lambda$ represents the Lorentz transformation matrix, then the transformation of contravariant components $x^\mu$ is given by $$x'^\mu=\Lambda^{\mu}{}_{\nu} x^\nu$$ and that of the covariant com …

Consider the energy-momentum tensor $$T_{\mu\nu}=(p+\rho)u_\mu u_\nu+pg_{\mu\nu}$$ used in Cosmology. I have a problem with this equation. Since this a tensor equation the RHS should transform in the …

In Weinberg's book of Qft, chapter 2 of volume 1, he uses the eigenstates of the four-momentum to construct the unitary irreducible representations of the Poincare group. My question is, since $P^\mu, …

My book claims that in vacuum, the total energy density of the electromagnetic field is equally shared between electric and magnetic fields by explicitly showing that $$\frac{1}{2}\epsilon_0 \textbf{E …

This question is based on Astrophysicist Thanu Padmanabhan's online lecture here, time around 13.00-14.00. Consider a map where the absolute time $t$ is mapped to another absolute time $f(t)$ i.e., $ …