Related papers: Categorical Foundation of Quantum Mechanics and St…
I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
The string theory defined by gauging $\W_{\infty/2}$, the sub-algebra of $\W_{\infty}$ generated by the currents of even spin, is discussed. The critical value of the central charge is calculated using zeta-function techniques and shown to…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
In this paper we give a contribution to the taxonomy of physical theories. We provide here a thorough description of the axiomatic foundations of the most relevant physical theories, Mechanics, Special Relativity, General Relativity,…
If the systems of quantum theory are thought of as elementary information carriers in the first place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than…
A quantum equivalence principle is formulated by means of a gravitational phase operator which is an element of the Poincare group. This is applied to the spinning cosmic string which suggests that it may, but not necessarily, contain…
Quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister, a system of qubits, representing a…
We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…
This contribution, aimed mostly at experimental particle physicists, reviews some of the main ideas and results of String Theory in a non-technical language. It originates from the talks presented by the authors at the Electro-Weak session…
Interpretation is not the only way to explain a theory's success, form and features, and nor is it the only way to solve problems we see with a theory. This can also be done by giving a reductive explanation of the theory, by reference to a…
String theory is changing the relationship between mathematics and physics. The central role is played by the phenomenon of duality, which is intrinsic to quantum physics and abundant in string theory.
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Superstring theory, and a recent extension called M theory, are leading candidates for a quantum theory that unifies gravity with the other forces. As such, they are certainly not ordinary quantum field theories. However, recent duality…
A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their…
It is shown that, with some reasonable assumptions, the theory of general relativity can be made compatible with quantum mechanics by using the field equations of general relativity to construct a Robertson-Walker metric for a quantum…
Recently, the author and Bob Coecke have introduced a categorical formulation of Quantum Mechanics. In the present paper, we shall use it to open up a novel perspective on No-Cloning. What we shall find, quite unexpectedly, is a link to…