Related papers: Factorization Rules in Quantum Teichm\"uller Theor…
The conventional phase space of classical physics treats space and time differently, and this difference carries over to field theories and quantum mechanics (QM). In this paper, the phase space is enhanced through two main extensions.…
We establish a form of the h-principle for the existence of foliations quasi-complementary to a given one; the same methods also provide a proof of the classical Mather-Thurston theorem.
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichm\"uller Space: (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The…
We highlight several analogies between the Finsler (infinitesimal) properties of Teichm\"uller's metric and Thurston's asymmetric metric on Teichm\"uller space. Thurston defined his asymmetric metric in analogy with Teichm\"ullers' metric,…
We consider finite temperature correlation functions in massive integrable Quantum Field Theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form…
We propose a geometric setting of the axiomatic mathematical formalism of quantum theory. Guided by the idea that understanding the mathematical structures of these axioms is of similar importance as was historically the process of…
We develop the quantum field theory of fermion mixing in curved spacetime and discuss the role of unitarily inequivalent representations in the particle interpretation of the theory. We derive general oscillation formulae and apply them to…
We construct a mathematical version of quantum field theory. It assigns to a multidimensional variational principle an associative algebra which is a quantization of the Poisson algebra of classical field theory observables. For free scalar…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
We study factorization algebras on configuration spaces of points on the curved, colored by elements of the root lattice. We show that the factorization algebra attached to Lusztig's quantum group can be obtained as a direct image of a…
We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…
We interpolate a new family of Teichm\"uller spaces $T_{\sharp}^X$ between the universal Teichm\"uller space $T$ and its little subspace $T_0$, which we call the Teichm\"uller space of piecewise symmetric homeomorphisms. This is defined by…
In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…
Thurston boundary of the universal Teichm\"uller space $T(\mathbb{D})$ is the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of $\mathbb{D}$. A geodesic ray in $T(\mathbb{D})$ is of generalized Teichm\"uller type…
Quantization of the Teichm\"uller space of a non-compact Riemann surface has emerged in 1980's as an approach to three dimensional quantum gravity. For any choice of an ideal triangulation of the surface, Thurston's shear coordinate…
Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of…
Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…