Non-existence of natural states for Abelian Chern–Simons theory

Dappiaggi, Claudio; Murro, Simone; Schenkel, Alexander

doi:10.1016/j.geomphys.2017.01.015

Cited by 15 publications

(11 citation statements)

References 8 publications

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“…We conclude this paper with an application of the results proven so far inspired by [17]. In loc.cit., the quantization of Abelian Chern-Simons theory is interpreted as a functor A : Man 2 Ñ STG-Alg which assigns symplectic twisted group ˚-algebras to 3-dimensional manifolds of the form R ˆΣ, where Σ is a 2-dimensional oriented manifold.…”

Section: G Is Torsion-freementioning

confidence: 52%

“…The K-symplectic abelian groups have been used in several topics, e.g. for K " Z in noncommutative geometry [10,18] and in abelian Chern-Simons theory [17], for K " R, C in quantum mechanics [1,26], in symplectic geometry and deformation quantization [11], for K " F p in modal quantum theory [52,53] and for K " Q p in p-adic quantum mechanics [63].…”

Section: ˆ0mentioning

confidence: 99%

“…In most of the models inspired by mathematical physics, the group of ˚-automorphisms is not compact nor Abelian, e.g. in abelian Chern-Simons theory, as studied in [17], E coincides with the symplectic group of automorphism. Nonetheless, it would be desirable to classify all the invariant states inasmuch they are interesting from mathematical and physical point of views.…”

Section: Introductionmentioning

confidence: 99%

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On the uniqueness of invariant states

Bambozzi,

Murro

2019

Preprint

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Section: G Is Torsion-freementioning

confidence: 52%

Section: ˆ0mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the uniqueness of invariant states

Bambozzi,

Murro

2019

Preprint

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“…Proposition 5.1) which play a pivotal rôle in the algebraic approach to linear quantum field theory, see e.g. [22,45] for textbooks, [8,9,17,43,48] for recent reviews, [18][19][20][21] for homotopical approaches and [23][24][25][30][31][32][33][34][35][36] for some applications. However, differently from [46,47], the Green operator will not have the usual support property due to the non-local behavior of the APS boundary condition.…”

Section: Introductionmentioning

confidence: 99%

The Cauchy problem of the Lorentzian Dirac operator with APS boundary conditions

Drago¹,

Große²,

Murro³

2021

Preprint

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We consider the classical Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to APS-boundary conditions. This is achieved by deriving suitable energy estimates, which play a fundamental role in establishing uniqueness and existence of weak solutions. Finally, by introducing suitable mollifier operators, we study the differentiability of the solutions. For obtaining smoothness we need additional technical conditions.

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“…Note that the zeroth homology H 0 (A CS (M )) is the ordinary algebra of gauge invariant observables for quantized flat R-connections, see e.g. [DMS17]. ▽ A Technical details for Section 6.2…”

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confidence: 99%

Algebraic field theory operads and linear quantization

Bruinsma

Schenkel

2019

Lett Math Phys

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We generalize the operadic approach to algebraic quantum field theory [arXiv:1709.08657] to a broader class of field theories whose observables on a spacetime are algebras over any singlecolored operad. A novel feature of our framework is that it gives rise to adjunctions between different types of field theories. As an interesting example, we study an adjunction whose left adjoint describes the quantization of linear field theories. We also analyze homotopical properties of the linear quantization adjunction for chain complex valued field theories, which leads to a homotopically meaningful quantization prescription for linear gauge theories.Keywords: algebraic quantum field theory, locally covariant quantum field theory, colored operads, universal constructions, gauge theory, model categories MSC 2010: 81Txx, 18D50, 18G55 F (G)/(r 1 = r 2 ) (2.5) in Op C (M). Example 2.6. Consider for the moment M = Set. The associative operad As ∈ Op { * } (Set) is the single-colored operad (i.e. C = { * } is a singleton) presented by the following generators and relations: We define the set of generators of arity n by G(n) :=      {η} , for n = 0 , {µ} , for n = 2 , ∅ , else , (2.6) for all n ≥ 0. The generator µ in arity 2 is interpreted as a multiplication operation and the generator η in arity 0 as a unit element. To implement associativity and left/right unitality of these operations, we consider R(n) :=      {λ, ρ} , for n = 1 , {a} , for n = 3 , ∅ , else , (2.7)

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Non-existence of natural states for Abelian Chern–Simons theory

Cited by 15 publications

References 8 publications

On the uniqueness of invariant states

On the uniqueness of invariant states

The Cauchy problem of the Lorentzian Dirac operator with APS boundary conditions

Algebraic field theory operads and linear quantization

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