Related papers: Topos-Theoretic Approaches to Quantum Theory
A topological quantum field theory is introduced which reproduces the Seiberg-Witten invariants of four-manifolds. Dimensional reduction of this topological field theory leads to a new one in three dimensions. Its partition function yields…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
In a recently proposed interpretation of quantum mechanics, U. Mohrhoff advocates original and thought-provoking views on space and time, the definition of macroscopic objects, and the meaning of probability statements. The interpretation…
We propose and develop the thesis that the quantum theoretical description of experiments emerges from the desire to organize experimental data such that the description of the system under scrutiny and the one used to acquire the data are…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…
In Phys. Rev. A 70, 032104 (2004), M. Montesinos and G. F. Torres del Castillo consider various symplectic structures on the classical phase space of the two-dimensional isotropic harmonic oscillator. Using Dirac's quantization condition,…
Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…
These are expanded notes of a course on basics of quantum field theory for mathematicians given by the author at MIT.
Different proposals for the wave function of the universe are analyzed, with an emphasis on various forms of the tunneling proposal. The issues discussed include the equivalence of the Lorentzian path integral and outgoing-wave proposals,…
The present short review article illustrates the latest theoretical developments on quantum tomography, regarding general optimization methods for both data-processing and setup. The basic theoretical tool is the informationally complete…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
This paper provides mathematical details related to another new paper which suggests: (1) new approaches to the analysis of soliton stability; (2) families of Lagrangian field theories where solitons might possibly exist even without…
I discuss topics in Particle Physics applying the novel ontological formulation of Relativistic Quantum Field Theory due to David Bohm. I argument that particle physicists might too benefit from this truly novel way of thinking Physics.
Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. Chern-Simons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots…
The paper puts together some loosely connected observations, old and new, on the concept of a quantum field and on the properties of Feynman amplitudes. We recall, in particular, the role of (exceptional) elementary induced representations…
These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…
This survey provides an introduction to the Stolz-Teichner program on elliptic cohomology and quantum field theory.
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
This is an introduction to type theory, synthetic topology, and homotopy type theory from a category-theoretic and topological point of view, written as a chapter for the book "New Spaces for Mathematics and Physics" (ed. Gabriel Catren and…
This chapter provides a review of the frameworks developed for cosmological perturbation theory in loop quantum cosmology, and applications to various models of the early universe including inflation, ekpyrosis and the matter bounce, with…