Related papers: On a Microscopic Representation of Space-Time V
A sketch is given of a circle of ideas relating quantum field theories with representation theory. The main mathematical ingredients are spinor geometry and the gauge group equivariant K-theory of the space of connections.
In recent years a new potential symmetry of fundamental particle physics has been investigated --- discrete quark-lepton symmetry. When this symmetry is implemented, however, it often leads to either of the unrealistic predictions…
The universal symmetry, or conservation, of complexity underlies any law or principle of system dynamics and describes the unceasing transformation of dynamic information into dynamic entropy as the unique way to conserve their sum, the…
Friedmann-Lemaitre equations with contributions coming from matter, curvature, cosmological constant, and radiation, when written in terms of conformal time u rather than in terms of cosmic time t, can be solved explicitly in terms of…
A mathematical framework for relativistic quantum field theory is constructed with natural symmetry $\mathsf{so}(2,3)= \mathsf{sp}(2,\mathbb{ R})$. In this framework gravity and electromagnetism unify as aspects of the geometry. The source…
In standard quantum theory, symmetry is defined in the spirit of Klein's Erlangen Program: the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the…
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be related to orientation, and its…
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…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. For static spherically symmetric space-times, the event horizon is coincident with a coordinate anomaly that introduces complications…
By using point-coupling versions of finite range nuclear relativistic mean field models containing cubic and quartic self interactions in the scalar field $\sigma$, a nonrelativistic limit is achieved. This approach allows an analytical…
We develop a systematic projector-based Feynman diagram framework that intrinsically encodes quantum geometry for nonlinear optical responses. By explicitly incorporating geometric quantities such as the quantum geometric tensor, quantum…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
Nielsen's geometric approach offers a powerful framework for quantifying the complexity of unitary transformations. In this formulation, complexity is defined as the length of the minimal geodesic in a suitably constructed geometric space…
Relativistic quantum field theory (QFT) is commonly formulated in terms of operators, asymptotic states, and covariant amplitudes, a perspective that tends to obscure the real-time origin of field dynamics and correlations. Here we…
We introduce new techniques for calculations in Gauge theories with extended supersymmetry. We are working in Projective Superspace where the $SU(2)$ R-symmetry is realized geometrically by including an auxilliary $\mathbb{CP}^1$ component…
Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based…
A quantum walk describes the discrete unitary evolution of a quantum particle on a discrete graph. Some quantum walks, referred to as the Weyl and Dirac quantum walks, provide a description of the free evolution of relativistic quantum…
Quantum states naturally represent symmetry groups, though often in a projective sense. Intriguingly, the projective nature of crystalline symmetries has remained underexplored until very recently. A series of groundbreaking theoretical and…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum…