Related papers: Quantum Field Theory, Quantum Geometry, and Quantu…
Supersymmetric theories are reviewed in the context of field theories. The gauge hierarchy problem in attempting the unification of all fundamental interactions is the strongest motivation of modern development of supersymmetry. Starting…
A novel algebraic topology approach to supersymmetry (SUSY) and symmetry breaking in quantum field and quantum gravity theories is presented with a view to developing a wide range of physical applications. These include: controlled nuclear…
We discuss the gauge natural formulation of supersymmetric theories and supergravity, with the aim to show that the standard and the supersymmetric frameworks admit in fact a unifying mathematical language.
We show that many well-known quantum field theories emerge as representations of a single $^\ast$-algebra. These include free quantum field theories in flat and curved space-times, lattice quantum field theories, Wightman quantum field…
Some ideas about phenomenological applications of quantum algebras to physics are reviewed. We examine in particular some applications of the algebras $U_ q (su_2)$ and $U_{qp}({\rm u}_2)$ to various dynamical systems and to atomic and…
In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and…
Over the past six years, a detailed framework has been constructed to unravel the quantum nature of the Riemannian geometry of physical space. A review of these developments is presented at a level which should be accessible to graduate…
We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge…
It is often overlooked that local quantum physics has a built in quantum localization structure which may under certain circumstances disagree with (differential, algebraic) geometric ideas. String theory originated from such a spectacular…
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have…
We discuss the possible applications supersymmetric theories might find in the field of elementary particle physics. The supersymmetric generalization of the $SU(3)\times SU(2)\times U(1)$ standard model is discussed in detail. Special…
The development of Noncommutative Geometry is creating a reworking and new possibilities in physics. This paper identifies some of the commutation and derivation structures that arise in particle and field interactions and fundamental…
Nuclear physics, whose underling theory is described by quantum gauge field coupled with matter, is fundamentally important and yet is formidably challenge for simulation with classical computers. Quantum computing provides a perhaps…
The phenomenon of quantum entanglement is thoroughly investigated, focussing especially on geometrical aspects and on bipartite systems. After introducing the formalism and discussing general aspects, some of the most important separability…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…
These are six papers joined by the same title. The main topics are: 1. algebraic nature of quantization of relativistic fields, 2. constructive definition of space of states of quantum electromagnetic field, 3. structure of space of states…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
We formulate the field-space geometry for an effective field theory of scalars and gauge bosons. Geometric invariants such as the field-space curvature enter in both scattering amplitudes and the renormalization group equations, with the…