Related papers: Gauge Theory Techniques in Quantum Cohomology

One of the main features of covariant theories, in particular general relativity, is that the field equation possesses gauge freedom associated with global diffeomorphisms of the underlying manifold. I shall explain here how the hole…

Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…

Associativity of the quantum product ensures flatness of the Dubrovin connection and is the basis for Hodge-theoretic mirror symmetry of Calabi-Yau threefolds. We use ring and module structure on cohomology pertaining to a Lagrangian…

A pedagogical introduction to some of the main ideas and results of field theories on quantized spacetimes is presented, with emphasis on what such field theories may teach us about the problem of quantizing gravity. We examine to what…

In a path-integral approach to quantum cosmology, the Lorenz gauge-averaging term is studied for Euclidean Maxwell theory on a portion of flat four-space bounded by two concentric three-spheres, but with arbitrary values of the gauge…

Decoherence of a quantum system (which then starts to display classical features) results from the interaction of the system with the environment, and is well described in the framework of the theory of continuous quantum measurements…

Using results of Gathmann, we prove the following theorem: If a smooth projective variety X has generically semisimple (p,p)-quantum cohomology, then the same is true for the blow-up of X at any number of points. This a successful test for…

Quantum Lefschetz theorem by Coates and Givental gives a relationship between the genus 0 Gromov-Witten theory of X and the twisted theory by a line bundle L on X. We prove the convergence of the twisted theory under the assumption that the…

The supersymmetric model developed by Witten to study the equivariant cohomology of a manifold with an isometric circle action is derived from the BRST quantization of a simple classical model. The gauge-fixing process is carefully…

A fibre bundle viewpoint of gauge field theories is reviewed with focus on a possible quantum interpretation. The fundamental quantum properties of non-separability of state spaces is considered in the context of defining the connection on…

Quantum metrology pursues high-precision measurements of physical quantities by using quantum resources. However, the decoherence generally hinders its performance. Previous work found that the metrological error tends to diverge in the…

We give a reformulation of the Dubrovin conjecture about the semisimplicity of quantum cohomology in terms of the so-called second structure connection of quantum cohomology. The key ingredient in our work is the notion of a twisted…

We construct a class of non-invertible duality defects, in (2+1)d quantum field theories, arising from half-spacetime gauging of a 2-group symmetry. Starting from a parent theory with two discrete and Abelian 0-form symmetries and a…

Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…

The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…

We give elementary proofs of the main theorems about (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, Siebert and Tian's presentation, and a recent theorem of…

We introduce functional degrees of freedom by a new gauge principle related to the phase of the wave functional. Thereby, quantum mechanical systems are seen as dissipatively embedded part of a nonlinear classical structure producing…

This paper introduces a general perturbative quantization scheme for gauge theories on manifolds with boundary, compatible with cutting and gluing, in the cohomological symplectic (BV-BFV) formalism. Explicit examples, like abelian BF…

Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type…

In the framework of Loop Quantum Cosmology, inhomogeneous models are usually quantized by means of a hybrid approach that combines loop quantization techniques with standard quantum field theory methods. This approach is based on a…