相关论文: Quantized Abelian principal connections on Lorentz…

Gauge-invariant quantum fields are constructed in an Abelian power-counting renormalizable gauge theory with both scalar, vector and fermionic matter content. This extends previous results already obtained for the gauge-invariant…

The content of two additional Ward identities exhibited by the $U(1)$ Higgs model is exploited. These novel Ward identities can be derived only when a pair of local composite operators providing a gauge invariant setup for the Higgs…

The study of dualities is a central issue in several modern approaches to quantum field theory, as they have broad consequences on the structure and on the properties of the theory itself. We call Abelian duality the generalisation to…

Let $X$ be a differentiable manifold endowed with a transitive action $\alpha:A\times X\longrightarrow X$ of a Lie group $A$. Let $K$ be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms…

By a diagonal embedding of $U(1)$ in $SU_q(m)$, we prolongate the diagonal circle action on the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ to the $SU_q(m)$-action on the prolongated bundle. Then we prove that the noncommutative vector…

We construct an action of 3-cobordisms on the finite dimensional Schr\"odinger representations of the Heisenberg group by Lagrangian correspondences. In addition, we review the construction of the abelian Topological Quantum Field Theory…

For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an…

A Q-manifold is a graded manifold endowed with a vector field of degree one squaring to zero. We consider the notion of a Q-bundle, that is, a fiber bundle in the category of Q-manifolds. To each homotopy class of ``gauge fields'' (sections…

Take a closed monotone symplectic manifold containing a smooth anticanonical divisor. The quantum connection on its cohomology has singularities at zero and infinity (in the quantum parameter). At zero it has a regular singular point, by…

Recent developments concerning canonical quantisation and gauge invariant quantum mechanical systems and quantum field theories are briefly discussed. On the one hand, it is shown how diffeomorphic covariant representations of the…

We examine quantum field theory in spacetimes that are time nonorientable but have no other causal pathology. These are Lorentzian universes-from-nothing, spacetimes with a single spacelike boundary that nevertheless have a smooth…

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As…

We consider a variant of the charge-Q compact Abelian-Higgs model, in which an Nf-dimensional complex vector is coupled with an Abelian Z_q gauge field. For Nf=2 and Q=1 we observe several transition lines that belong to the O(4), O(3), and…

We show that a vector space valued TQFT constructed in work of De Renzi et al. [DGGPR23] extends naturally to a topological field theory which takes values in the symmetric monoidal category of linear cochains. Specifically, we consider a…

Let $\mathfrak{g}$ be a simple complex Lie algebra of a classical type and $U_q(\mathfrak{g})$ the corresponding Drinfeld-Jimbo quantum group at $q$ not a root of unity. With every point $t$ of the fixed maximal torus $T$ of an algebraic…

The notion of a translation map in a quantum principal bundle is introduced. A translation map is then used to prove that the cross sections of a quantum fibre bundle $E(B,V,A)$ associated to a quantum principal bundle $P(B,A)$ are in…

In the foundational logical framework of homotopy-type theory we discuss a natural formalization of secondary integral transforms in stable geometric homotopy theory. We observe that this yields a process of non-perturbative cohomological…

We construct pairs of compact K\"ahler-Einstein manifolds $(M_i,g_i,\omega_i)$ ($i=1,2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_i=\bigwedge^n T^*M_i$ has Chern class $[\omega_i/2\pi]$, and for…

A generalisation of the equivariant Dixmier-Douady invariant is constructed as a second-degree cohomology class within a new semi-equivariant \v{C}ech cohomology theory. This invariant obstructs liftings of semi-equivariant principal…

A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…