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The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

1
vote
1answer
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 …
asked Nov 27 '16 by SRS
7
votes
2answers
Is it possible to construct an adjoint representation for the Lorentz group?
asked Feb 13 '14 by SRS
0
votes
1answer
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 …
asked Feb 17 '16 by SRS
1
vote
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 …
answered Oct 13 '16 by SRS
0
votes
1answer
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 …
asked Jan 6 '17 by SRS
0
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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. …
answered Apr 10 '18 by SRS
1
vote
2answers
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 …
asked Dec 26 '17 by SRS
12
votes
3answers
In non-relativistic quantum mechanics, causality is violated by saying that the amplitude of propagation of a particle $$A=\langle \textbf{x}|\exp{\Big(\frac{-i\textbf{p}^2t}{2m\hslash}}\Big)|\textbf{ …
asked Sep 24 '17 by SRS
3
votes
2answers
Why is it said that the cut-off regularization is not a Lorentz invariant regularization method?
asked Jun 24 '15 by SRS
0
votes
1answer
In the metric convention $(+,-,-,-)$, the spacetime interval is given by $$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 …
asked Jan 25 '17 by SRS
3
votes
1answer
The conserved charge associated with the Lorentz transformation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ a …
asked Feb 6 '14 by SRS
4
votes
2answers
The group of Mobius transformations, denoted by ${\rm Mob}(2,\mathbb{C})$, is isomorphic to ${\rm SL}(2,\mathbb{C}))/\mathbb{Z}_2$ which in turn is isomorphic to the Lorentz group ${\rm SO}^+(3,1)$. …
asked Jan 14 '18 by SRS
1
vote
Following the discussion with AcuriousMind, my current understanding is that the set of functions $\{e^{ik\cdot x}\}$ (stationary solutions of KG equation) do not form a complete set if we exclude neg …
answered Mar 25 '18 by SRS
9
votes
3answers
How can it be shown that the Dirac spinor is the direct sum of a right-handed Weyl spinor and a left-handed Weyl spinor? EDIT: - Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed …
asked Jan 27 '14 by SRS
4
votes
1answer
The one-particle states in the Hilbert space of a quantized relativistic field theory are said to form irreducible representations of the Poincaré group. Why is that? I mean, popular texts in QFT do …
asked Dec 18 '15 by SRS

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