Algebraic Topology Foundations of Supersymmetry and Symmetry Breaking in Quantum Field Theory and Quantum Gravity: A Review

Abstract

Abstract. 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 fusion and other nuclear reaction studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller effects, superfluidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions and supergravity. This approach requires a unified conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of nonAbelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. Fourier transforms, generalized FourierStieltjes transforms, and duality relations link, respectively, the quantum groups and quantum groupoids with their dual algebraic structures; quantum double constructions are also discussed in this context in relation to quasi-triangular, quasi-Hopf algebras, bialgebroids, Grassmann-Hopf algebras and higher dimensional algebra. On the one hand, this quantum algebraic approach is known to provide solutions to the quantum Yang-Baxter equation. On the other hand, our novel approach to extended quantum symmetries and their associated representations is shown to be relevant to locally covariant general relativity theories that are consistent with either nonlocal quantum field theories or local bosonic (spin) models with the extended quantum symmetry of entangled, 'string-net condensed' (ground) states. I.C. Baianu, J.F. Glazebrook and R. BrownKey words: extended quantum symmetries; groupoids and algebroids; quantum algebraic topology (QAT); algebraic topology of quantum systems; symmetry breaking, paracrystals, superfluids, spin networks and spin glasses; convolution algebras and quantum algebroids; nuclear Fréchet spaces and GNS representations of quantum state spaces (QSS); groupoid and functor representations in relation to extended quantum symmetries in QAT; quantization procedures; quantum algebras: von Neumann algebra factors; paragroups and Kac algebras; quantum groups and ring structures; Lie algebras; Lie algebroids; GrassmannHopf, weak C * -Hopf and graded Lie algebras; weak C * -Hopf algebroids; compact quantum groupoids; quantum groupoid C * -algebras; relativistic quantum gravity (RQG); supergravity and supersymmetry theories; fluctuating quantum spacetimes; intense gravitational fields; Hamiltonian algebroids in quantum gravity; Poisson-Lie manifolds and quantum gravity theories; quantum fundamental groupoids; tensor products of algebroids and categories; quantum double groupoids and algebroids; higher dimensional quantum symmetries; applications of generalized van Kampen theorem (GvKT) to quantum spacetime invariants

Generalized Chemical Block Systems on Chern-Simons φ∘ D∘ r2∘ S∘ r1 Topologies for the generation of the Roccustyrna Holomorphic Ligand.

“…one ((2r, 5r) -5 -(2 -methyl -6 -methylidene -6, 9 -dihydro -3H -purin -9 -yl) -3 -methylideneoxolan -2 -yl) phosphirane -1 -carbonitrile -oxy} imino) -1lambda5, 2lambda5 -azaphosphiridin -1 -ylium input of a fragmented compounds in the next pharmacophoric system B: S4 -cyano -1 -({ ((2S, 4r, 5r) -2methyl -2 -2 -({ ( uoro ({ ((2E) -5 -oxabicyclo (2.1.0) pentan -2 -ylidene) cyano -lambda6 -sulfanyl}) methyl) phosphorylidene} amino) S4 -cyano -1 -({ ((2S, 4r, 5r) -2 -methyl -2 -2 -({ ( uoro ({ ((2E) -5 -oxabicyclo (2.1.0) pentan -2 -ylidene) cyano -lambda6 -sulfanyl}) methyl) phosphorylidene} amino) -4, 6dihydro -1H -purin -6 -one (methylamino) -1, 6 -diazabicyclo (3.2.0) heptan -4 -yl) (1S, 2r, 3S) -2 -({ ((1S, 2S, 4S, 5r) -4 -ethenyl -4 -sulfonylbicyclo (3.2.0) heptan -2 -yl) oxy} amino) -3 -2 -({ ( uoro ({ ((2E) -5 -oxabicyclo (2.1.0) pentan -2 -ylidene) cyano -lambda6 -sulfanyl}) methyl) phosphorylidene} amino) -4, 6 -dihydro -1H -purin -6 -one ((2r, 5r) -5 -(2 -methyl -6 -methylidene -6, 9 -dihydro -3H -purin -9 -yl) -3 -methylideneoxolan -2 -yl) phosphirane -1carbonitrile -oxy} imino) -1lambda5, 2lambda5 -azaphosphiridin -1 -ylium -4, 6 -dihydro -1H -purin -6 -one (methylamino) -1, 6 -diazabicyclo (3.2.0) heptan -4 -yl) (1S, 2r, 3S) -2 -({ ((1S, 2S, 4S, 5r) -4 -ethenyl -4 -sulfonylbicyclo (3.2.0) heptan -2 -yl) oxy} amino) -3 -2 -({ ( uoro ({ ((2E) -5 -oxabicyclo (2.1.0) pentan -2 -ylidene) cyano -lambda6 -sulfanyl}) methyl) phosphorylidene} amino) -4, 6 -dihydro -1H -purin -6 -one ((2r, 5r) -5 -(2 -methyl -6methylidene -6, 9 -dihydro -3H -purin -9 -yl) -3 -methylideneoxolan -2 -yl) phosphirane -1 -carbonitrile -oxy} imino) -1lambda5, 2lambda5azaphosphiridin -1 -ylium αk represents the parameters of displacement D (α (k)) and φ (•) is nonlinear function. (42,43,44,45,46) The holomorphic chemical block has appeared before in this paper, in several different guises. In particular, it agrees -up to our standard projective factors expπ2~ Q + C + ~ Q -with the direct analytic continuation of the trefoil's colored Jones polynomial, computed by q −1 cˆ −1/2Mˆ −2 Ψ(eU In principle, a Chern -Simons anti -de Sitter supergravity can be constructed from the knowledge of the associated supergroup and an invariant tensor only ( nding the invariant tensor, however, may prove to be a non -trivial task).…”

Avogadro Number’s-oriented HyperGeometric and ChebyshevT Functions for Black Hole Paradox Generalizations and Turing Machine Ruled Quantum Homeopathy Water Memory Entanglements for the Translation of COVID19 Homeopathy Remedies into the Neprilysin and ACE

“…The second component Θ of this pair is the reconstructed (and non-unique) metric that represents a protein-ligand complexes using a regular 3D grid with voxels characterized by pharmacophoric features of nearby atom types. While there is substantial evidence supporting reductions in docking energy and binding affinity scoring values [1-37, , evidence of generalization performance under certain constructions of edges also exists (e.g., 195]) which may be partly attributable to shallower quantum circuits providing better utility bounds than deeper circuits , and constraints with classical neural network intuition with increased layer depth and with an exponential increase in model expressiveness [94][95][96][97][98][99][100][101][102][103][104][105][106][107][108]. This historical detour let us remind the readers that nuclear physicists opened this Pandora's box twenty years ago when considering fermionic Hamiltonians h (acting in complicated Fock's space H(P) of "physical" states |ψ (P) i) as transformed into isospectral operators H (acting in another "friendly" space H(F)) which can be easily be combined with a topological string field theory analysis similar to the one given earlier in a heuristic sense, since it is supported by a rigorous mathematical framework due to the uncertainty relation, between two spheres of radius nr and n ✷ respectively, since also 𝐶 ̂ ∞ operations imply infinitely many operations.…”

The free energy principle induces neuromorphic development

“…The relevant symmetry is then either individuated by some Lie group or by some quantum group, namely a non-trivial Hopf-algebra [193,194] (see e.g. [195] for a review of some general extensions of these topics). TQNNs are then represented as superpositions of the basis elements on the boundary sector B. Spin-networks provide an orthonormal basis, but is worth reminding that loop states as well span the Hilbert space of quantum states over B, and that a unitary transform exists [196] that connects the two classes of states.…”