All Questions
Tagged with hilbert-spaces quantum-field-theory
8 questions
2
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Representations of the commutation relations and renormalization
I had a hard time deciding whether this question is more appropriate for physicsSE or MO, so I have cross-listed it for the time being. The physicsSE post can be found here.
In the lecture Is ...
- 721
6
votes
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Identification of Fock space and the $L^2$ space of tempered distributions
Let $\mathcal{S}'(\mathbb{R}^d)$ be the set of tempered distributions over $\mathbb{R}^d$ and $d\phi_C$ a Gaussian measure over $\mathcal{S}'(\mathbb{R}^d)$ with covariance operator $C$. Consider the ...
- 721
2
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Ultraviolet divergences of entanglement entropy in QFT
I've often read that entanglement entropy in quantum field theory is ill-defined because local algebras are generally of type III, which implies that a trace doesn't exist. For a normal state $\omega_{...
- 424
5
votes
1
answer
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Initial conditions in the Klein-Gordon equation
I am interested in what are the largest families of initial conditions of the problem (in $\mathbb{R}^{4}$)
\begin{equation}\label{kg}
\left\lbrace
\begin{array}{ll}
(\square+m^2)F(x)=0\\
...
- 424
3
votes
2
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411
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Spin-statistic for free quantum fields
Short version of the question:
Can someone explains what physicist's 'Spin-statistic theorem' says rigorously in the context of Free Quantum fields when they are describe as the Fock space of some '1-...
- 42.4k
2
votes
1
answer
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Representation of an arbitrary element on a fermionic Fock Space
Let $\mathcal{H}$ be a Hilbert space with orthonormal basis $\{\varphi_{k}\}_{k\in I}$. Take $\mathcal{H}^{\otimes n} := \overbrace{\mathcal{H}\otimes\cdots\otimes \mathcal{H}}^{\mbox{$n$ times}}$. An ...
- 1,305
9
votes
2
answers
746
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Characters of irreducible unitary representations of the Poincaré group
Consider Poincare group $\mathrm{ISO}(1,d-1)$, given by $\mathbb R^{1,d-1}\rtimes SO(1,d-1)$ in signature $(1,d-1)$, for some odd $d \geq 3$.
Denote the universal cover of the component connected to ...
- 533
2
votes
2
answers
700
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Quantum Field theory - integral notation
I have a problem with understanding how the resolution of the identity of an operator is presented in some literature for physicists.
I'm a student of mathematics, and I understand the notion of a ...
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