相关论文: Factorial Representations of Compact Lie Groups, W…

We develop a new mathematical approach to diffeomorphism invariant quantum states for the quantisation of general field theories such as general relativity and modified gravity. Treating quantum fields as fibre bundles, we discuss operators…

Unitary Representations corresponding to local shifts in reference frames are a key topic for progress in Quantum Gravity. The fibre bundle construct defined in our previous work in which quantum fields become liftings of; or sections…

Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical…

We develop further our fibre bundle construct of non-commutative space-time on a Minkowski base space. We assume space-time is non-commutative due to the existence of additional non-commutative algebraic structure at each point x of…

Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in…

The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a…

We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…

This paper clarifies the local structure of the energy representation of a local gauge group. The group to be considered is a smooth map from a manifold into a compact Lie group. It acts on a Boson Fock spaces generated by connection…

In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the…

In the present paper we review in a fibre bundle context the covariant and massless canonical representations of the Poincare' group as well as certain unitary representations of the conformal group (in 4 dimensions). We give a simplified…

Given a symmetry group acting on a principal fibre bundle, symmetric states of the quantum theory of a diffeomorphism invariant theory of connections on this fibre bundle are defined. These symmetric states, equipped with a scalar product…

Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of…

We introduce a certain type of representations for the quantum Teichmuller space of a punctured surface, which we call local representations. We show that, up to finitely many choices, these purely algebraic representations are classified…

The coadjoint orbits of compact Lie groups each carry a canonical (positive definite) K\"ahler structure, famously used to realize the group's irreducible representations in holomorphic sections of appropriate line bundles (Borel-Weil…

Within the setting of a recently proposed model of quantum fields on noncommutative Minkowski spacetime, the consequences of the consistent application of the proper, untwisted Poincare group as the symmetry group are investigated. The…

Employing the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables…

Let $(M,g)$ be a smooth Riemannian manifold, $K$ a compact Lie group and $p:P\to M$ a principal $K$-bundle over $M$ endowed with a connection $A$. Fixing a bi invariant inner product on Lie algebra $\mathfrak{k}$ of $K$, the connection $A$…

This paper deals with affine connections on real manifolds. We give a new characterization of flat affine connections on real manifolds by means of certain affine representations of the Lie group of automorphisms preserving the connection.…

We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of…

We investigate the properties of the inverse limit of the algebras of local unitary invariant polynomials of quantum systems containing various types of fermionic and/or bosonic particles as the dimensions of the single particle state…