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Results tagged with quantum-field-theory
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user 150264
For questions about mathematical problems arising from quantum field theory, the branch of physics which describes subatomic particles and their interactions in terms of perturbations of the corresponding scalar, vector or tensor fields.
6
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2
answers
639
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Explicit form of this unitary transformation
Disclaimer: This question has its motivation from physics. It is probably not entirely rigorous at the moment. I just want to clarify some steps and try to make the arguments rigorous afterwards, if p …
CommunityBot
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2
votes
1
answer
173
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The ultraviolet limit as a limiting case of the renormalization group flow?
In his paper Constructive Renormalization Theory, V. Rivasseau describes the idea of Wilson's approach of solving path integrals step by step. In section 1.4, page 5, however, there is a statement whi …
8
votes
1
answer
981
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Rigorous construction of fermionic field theory?
In section X.7 of Reed & Simon's book there is a nice rigorous construction of the free scalar field theory which applies to the Klein-Gordon field.
Question: Are there references which discuss, in an …
- 7,817
5
votes
1
answer
494
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Can Fock spaces be replaced by arbitrary Hilbert spaces under some hypothesis to justify pat...
I was reading this post from PSE and it reminded me an old question of mine, in which the use of creation and annihilation operators were discussed. Both questions got answers which agreed on the fact …
- 6,367
0
votes
0
answers
65
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Slice in momentum space?
This is probably a very basic question but I tried physics stack exchange already and I got no answers, so I'm asking the same question here.
I was reading this article and the author considers the fo …
- 3,535
8
votes
1
answer
211
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From the conceptual idea of the RG to its actual implementation
Everytime I want to understand a little more about the ideas behind Renormalization Group techniques, I get troubled by a gap between the general picture one usually presents (e.g. in books or pedagog …
- 188k
18
votes
3
answers
4k
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QFT and mathematical rigor
One way to approach QFT in mathematical terms is provided by the so-called Gårding-Wightman axioms, which defines in rigorous mathematical terms what a quantum field theory is supposed to be. If I'm n …
- 203
6
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0
answers
286
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Two questions about Fock spaces
Let $\mathscr{H}$ be a complex Hilbert space and denote $\mathscr{H}_{n}$ the tensor product $\overbrace{\mathscr{H}\otimes\cdots\otimes\mathscr{H}}^{\text{n}}$. Denote by $\Pi_{\pm}$ the projection o …
- 3,535
2
votes
0
answers
237
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Frontiers of QM and QFT
This is somehow a more mature version of an old question of mine. I'd like to have a more clear picture of the difference between QFT and QM from a mathematical point of view.
Okay, so we begin with a …
- 3,535
3
votes
0
answers
122
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Construction of Dirac field theory
In what follows, I'm following Folland's book and Reed & Simon.
Notation: Points in $\mathbb{R}^{4}$ are denoted by $p =(p_{0},p_{1},p_{2},p_{3})$. Also, I'm using Reed & Simon's notation for the Lore …
- 3,535
1
vote
1
answer
276
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Invariance of Lorentz measure
Let $m > 0$ be fixed. If $x=(x_{0},x_{1},x_{2},x_{3})$ and $y = (y_{0},y_{1},y_{2},y_{3})$ are elements of $\mathbb{R}^{4}$, we denote the Lorentz inner product by:
$$ x\cdot \tilde{y} := x_{0}y_{0}-x …
- 391
11
votes
2
answers
1k
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Axiomatic QFT, the reconstruction theorem and functional integrals
Before posting my question, let me make some remarks:
[MS] Salmhofer's book on renormalization begins with a nice discussion on Feynman's path integral. At some point, the author states the following: …
- 3,065
4
votes
1
answer
602
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Representations of the Lorentz group
The first few lines of this post is based on this lecture notes, but similar expositions can be found in other physics books such as Peskin & Schroeder's book.
On chapter 8 of the linked notes, the au …
- 21.5k
3
votes
1
answer
274
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Free field rigorous quantization - possibly a misunderstanding?
I'm sorry if this is not the right place to ask this question but I've been struggling with this for days now (and I think this is too technical/specific for math stack).
Notation: A conjugation $C$ o …
- 3,535
2
votes
Free field rigorous quantization - possibly a misunderstanding?
I think I figured it out. Let $f \in \mathscr{H}$ be arbitrary, where $\mathscr{H}$ here is a complex Hilbert space. Then $f$ can be written uniquely as:
$$f = f_{1} + if_{2} $$
where $f_{1},f_{2} \in …
- 3,535