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Results tagged with mp.mathematical-physics
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user 150264
Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.
39
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4
answers
5k
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Interesting and surprising applications of the Ising Model
One of the most famous models in physics is the Ising model, invented by Wilhelm Lenz as a PhD problem to his student Ernst Ising. The one-dimensional version of it was solved in Ising's thesis in 192 …
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20
votes
2
answers
7k
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Question about functional derivatives
This page on Wikipedia defines the so-called functional derivative as follows: "Given a manifold $M$ representing (continuous/smooth) functions $\rho$ (with certain boundary conditions, etc.) and a fu …
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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 …
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16
votes
2
answers
2k
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Good overviews on $\phi^{4}$-field theory?
I'm looking for nice overviews on $\phi^{4}$-field theory from the mathematical-physics point of view. To be a little more specific, here are some topics I'd like to read about:
(1) What are the motiv …
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14
votes
2
answers
941
views
How are Clifford algebras and spinors used to study the Ising model?
I've heard Clifford algebras and spinors are useful tools to study the Ising model, but I've never find any good discussion on this matter. Also, as far as I know, in the original solutions of the 2-D …
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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: …
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10
votes
0
answers
392
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Is there a general theory for Wilsonian renormalization?
I know that Wilson's renormalization group is not a theory per se and that there are many ways to implement it in a given system. Also, renormalization group techniques are applied in a large number o …
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9
votes
2
answers
2k
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Is $C^{*}$-algebra the most modern way to study QFT?
I am not an expert on either QFT or $C^{*}$-algebras, but I'm trying to learn the basics of QFT. In all books/papers and other materials that I know, QFT is studied mainly using a lot of functional an …
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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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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 …
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8
votes
2
answers
1k
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Creation and annihilation operators in QFT
As I said before, I'm not a QFT expert but I'm trying to understand the basics of its rigorous formulation.
Let's take Dimock's book, where the foundation of QM and QFT is discussed. If we consider, s …
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6
votes
2
answers
589
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Reference for rigorous second quantization
I'd like to get acquainted with the basics of mathematical rigorous second quantization, so I'm looking for an adequate reference on this subject. I've a background in quantum mechanics, but I don't k …
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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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6
votes
1
answer
701
views
Invertibility of discrete Laplacian
In QFT and Statistical Mechanics the discrete Laplacian usually plays a key role when we want to discretize the theory. However, few books (at least to my knowledge) really work the properties of this …
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6
votes
2
answers
865
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Gaussian measure on function spaces
I'm reading this classic work and I'd like to get deeper inside some of its techniques. In particular, the authors state: "We construct a Gaussian measure $d\mu_{0}(\phi)$ on a measure space of contin …
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