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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
votes
2
answers
639
views
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 …
- 3,535
2
votes
1
answer
173
views
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 …
- 3,535
5
votes
1
answer
494
views
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 …
- 3,535
0
votes
0
answers
65
views
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
views
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 …
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6
votes
0
answers
286
views
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 …
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2
votes
0
answers
237
views
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
views
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
views
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:
$$ x\cdot \tilde{y} := x_{0}y_{0}-x …
- 3,535
18
votes
3
answers
4k
views
QFT and mathematical rigor
One way to approach QFT in mathematical terms is provided by the so-called Gårding-Wightman axioms, which defines in rigorous mathematical terms what a quantum field theory is supposed to be. If I'm n …
- 3,535
8
votes
1
answer
981
views
Rigorous construction of fermionic field theory?
In section X.7 of Reed & Simon's book there is a nice rigorous construction of the free scalar field theory which applies to the Klein-Gordon field.
Question: Are there references which discuss, in an …
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4
votes
1
answer
602
views
Representations of the Lorentz group
The first few lines of this post is based on this lecture notes, but similar expositions can be found in other physics books such as Peskin & Schroeder's book.
On chapter 8 of the linked notes, the au …
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2
votes
Free field rigorous quantization - possibly a misunderstanding?
I think I figured it out. Let $f \in \mathscr{H}$ be arbitrary, where $\mathscr{H}$ here is a complex Hilbert space. Then $f$ can be written uniquely as:
$$f = f_{1} + if_{2} $$
where $f_{1},f_{2} \in …
- 3,535
3
votes
1
answer
274
views
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
5
votes
1
answer
355
views
How can one recover/obtain information from the renormalization group procedure?
I know the basic idea behind the renormalization group approach as it is used in mathematical physics to study both QFT and statistical mechanics. However, I have trouble understanding how can one rec …
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