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Results tagged with quantum-field-theory
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user 11211
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.
21
votes
Accepted
QFT and mathematical rigor
As Abdelmalek Abdesselam pointed in his comment to the OP, the axiomatic approach to QFT is rather concerned with answering the question "what is a quantum field?". This is stated right at the Preface …
- 7,817
17
votes
Accepted
References request: constructive quantum field theory
The standard reference for constructive QFT is the classic book by J. Glimm and A. Jaffe, Quantum Physics: a Functional Integral Point of View (2nd. ed., Springer-Verlag, 1988). It is certainly more t …
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16
votes
Accepted
Rigorous construction of fermionic field theory?
There is the construction of the C${}^*\!$-algebra of canonical anticommutation relations (CAR's), which is actually somewhat easier than the construction of free bosonic fields: given any complex pre …
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13
votes
Accepted
C*-algebras and quantum fields
The Weyl algebra construction can be done abstractly for any real vector space (even infinite-dimensional) endowed with an antisymmetric bilinear form, thanks to B. Blackadar's universal C*-algebra co …
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10
votes
What mathematical treatment is there on the renormalization group flow in a space of Lagrang...
A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent (originally two-part, now turned into three-part) exposition by Jonathan Dimock, av …
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9
votes
Accepted
Initial conditions in the Klein-Gordon equation
One must remark that derivatives in Sobolev spaces are usually taken in the sense of distributions: given $k\in\mathbb{N}_0=\{0,1,2,\ldots\}$, $H^k(\mathbb{R}^n)$ is the space of tempered distribution …
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9
votes
Accepted
Is there, mathematically speaking, a QFT with the following properties?
First of all, strictly speaking you are talking about a finite-dimensional (in fact, 2-dimensional) caricature of QFT. More precisely, the only way in which your model can be thought of as a QFT is if …
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5
votes
Accepted
Wick product of free fields and wave front sets in the sense of Lars Hörmander
The answer to both questions is no. This is due to two facts:
The Klein-Gordon two-point distribution $\omega_2(x,y)=\langle\Omega,\phi(x)\phi(y)\Omega\rangle$ in $\mathbb{R}^4$, where $\Omega_1=\Ome …
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4
votes
Quantum fields and infinite tensor products
The "infinite tensor product" picture may be useful as a sort of concrete image of the state space of a quantum field theory, but in practice is rarely used because of the technical difficulties it br …
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4
votes
Reference request for a treatment of Schwinger–Dyson equations
In the formulation of QFT using formal functional integrals, as mentioned by Igor in his answer, the Schwinger-Dyson equation becomes an infinite-dimensional differential equation for the partition fu …
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2
votes
Accepted
Extracting each field operator as Wightman fields from a set of time-ordered products satisf...
The same paper shows that the converse is true: starting from time-ordered Green functions satisfying axioms T1-T7 as in subsection I.1 one can get the Schwinger functions (Theorem 1, pp. 99, add Coro …
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1
vote
Braided Hopf algebras and Quantum Field Theories
Braided monoidal categories - more precisely, C*-categories of such kind - are the basic mathematical tool to encode the structure of superselection sectors in low-dimensional (<4) QFT. The low dimens …
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