Local conformal symmetry: The missing symmetry component for space and time

2015 ◽  
Vol 24 (12) ◽  
pp. 1543001 ◽  
Author(s):  
Gerard ’t Hooft
Keyword(s):  
Gravitational Force ◽  
Lorentz Invariance ◽  
Conformal Symmetry ◽  
Planck Scale ◽  
Small Distance ◽  
Approximate Symmetry ◽  
Complete Understanding ◽  
Yang Mills ◽  
Space And Time ◽  
Exact Symmetry

Local conformal symmetry is usually considered to be an approximate symmetry of nature, which is explicitly and badly broken. Arguments are brought forward here why it has to be turned into an exact symmetry that is spontaneously broken. As in the BEH mechanism in Yang–Mills theories, we then will have a formalism for disclosing the small-distance structure of the gravitational force. The symmetry could be as fundamental as Lorentz invariance, and guide us towards a complete understanding of physics at the Planck scale.

scholarly journals Trace dynamics and division algebras: towards quantum gravity and unification

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Lie Group ◽  
Planck Scale ◽  
The Self ◽  
Division Algebras ◽  
Quantum Field ◽  
Octonion Algebra ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Massless Spin ◽  
Correct Understanding

AbstractWe have recently proposed a Lagrangian in trace dynamics at the Planck scale, for unification of gravitation, Yang–Mills fields, and fermions. Dynamical variables are described by odd-grade (fermionic) and even-grade (bosonic) Grassmann matrices. Evolution takes place in Connes time. At energies much lower than Planck scale, trace dynamics reduces to quantum field theory. In the present paper, we explain that the correct understanding of spin requires us to formulate the theory in 8-D octonionic space. The automorphisms of the octonion algebra, which belong to the smallest exceptional Lie group G2, replace space-time diffeomorphisms and internal gauge transformations, bringing them under a common unified fold. Building on earlier work by other researchers on division algebras, we propose the Lorentz-weak unification at the Planck scale, the symmetry group being the stabiliser group of the quaternions inside the octonions. This is one of the two maximal sub-groups of G2, the other one being SU(3), the element preserver group of octonions. This latter group, coupled with U(1)em, describes the electrocolour symmetry, as shown earlier by Furey. We predict a new massless spin one boson (the ‘Lorentz’ boson) which should be looked for in experiments. Our Lagrangian correctly describes three fermion generations, through three copies of the group G2, embedded in the exceptional Lie group F4. This is the unification group for the four fundamental interactions, and it also happens to be the automorphism group of the exceptional Jordan algebra. Gravitation is shown to be an emergent classical phenomenon. Although at the Planck scale, there is present a quantised version of the Lorentz symmetry, mediated by the Lorentz boson, we argue that at sub-Planck scales, the self-adjoint part of the octonionic trace dynamics bears a relationship with string theory in 11 dimensions.

Classical fields in curved spacetime

2021 ◽  
pp. 294-313
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Vector Fields ◽  
Lorentz Invariance ◽  
Conformal Symmetry ◽  
Scalar Fields ◽  
Gauge Fields ◽  
Curved Spacetime ◽  
Curved Space ◽  
Spinor Fields ◽  
Vector Gauge ◽  
Classical Fields

This chapter discusses classical fields in an arbitrary Riemann spacetime. General considerations are followed by the formulation of scalar fields with non-minimal coupling. Spontaneous symmetry breaking in curved space is shown to provide the induced gravity action with a cosmological constant. The construction of spinor fields in curved spacetime is based on the notions of group theory from Part I and on the local Lorentz invariance. Massless vector fields (massless vector gauge fields) are described and the interactions between scalar, fermion and gauge fields formulated. A detailed discussion of classical conformal transformations and conformal symmetry for both matter fields and vacuum action is also provided.

Wave Function Collapse as a Real Physical Phenomenon Caused by Vacuum Fluctuations Near the Planck Scale

1991 ◽  
Vol 46 (9) ◽  
pp. 746-758 ◽  
Author(s):  
F. Winterberg
Keyword(s):  
Wave Function ◽  
Phase Velocity ◽  
Lorentz Invariance ◽  
Physical Phenomenon ◽  
Planck Scale ◽  
Quantum Mechanical ◽  
Vacuum Fluctuations ◽  
Gauge Bosons ◽  
Proposed Model ◽  
Wave Modes

AbstractIt is hypothesized that the collapse of the wave function is a real physical phenomenon caused by vacuum fluctuations near the Planck scale. The hypothesis is suggested by a recently proposed model (Planck aether model) according to which the fundamental kinematic symmetry is the Galilei-group with the Lorentz invariance as a derived dynamic symmetry. The proposed model has the goal to derive all fields and their interactions from an exactly nonrelativistic operator field equation, resembling Heisenberg's relativistic spinor field equation. In this model the groundstate of the vacuum is a superfluid consisting of an equal number of positive and negative Planck masses interacting via delta function potentials and making the cosmological constant equal to zero. Gauge bosons come from transverse waves propagating in a lattice of quantized vortices, and spinors are explained in this model as exciton-like quasiparticles held together by gauge bosons. Because vector gauge bosons move in the model with the velocity of light, objects held together by the forcc fields of these bosons obey Lorentz invariance as a dynamic symmetry. With the longitudinal wave modes moving with a superluminal phase velocity at energies near the Planck scale, it is conjectured that the quantum mechanical wave function is real and that its collapse results from the entrapment of the wave function by these longitudinal superluminal wave modes. Because these modes occur near the Planck scale their very large zero point fluctuations might therefore trigger the collapse even through dense matter. But because the fluctuations are finite, and because the wave modes have a finite albeit very large phase velocity, the quantum mechanical correlations would be broken above a ccrtain finite length. In the limit of a vanishing Planck length, and hence vanishing gravitational constant G, the phase velocity would become infinite, and the same would be true for the length above which the correlations are broken. One therefore may say that in the limit G = 0 the collapse is infinitely fast and that in this limit the correlations are not broken even over arbitrarily large distances

scholarly journals Softly broken conformal symmetry and the stability of the electroweak scale

2015 ◽  
Vol 30 (02) ◽  
pp. 1550006 ◽  
Author(s):  
Piotr H. Chankowski ◽  
Adrian Lewandowski ◽  
Krzysztof A. Meissner ◽  
Hermann Nicolai
Keyword(s):  
Field Theory ◽  
Standard Model ◽  
Conformal Symmetry ◽  
Planck Scale ◽  
Effective Field ◽  
Effective Theory ◽  
Minimal Extension ◽  
Fundamental Theory ◽  
Hierarchy Problem ◽  
Physical Scale

We point out a possible mechanism by which the electroweak hierarchy problem can be avoided in the low energy effective quantum field theory. Assuming the existence of a UV complete underlying fundamental theory and treating the cutoff scale Λ of the effective field theory as a real physical scale we argue that the hierarchy problem would be solved if the coefficient in front of quadratic divergences vanished at the scale Λ, and if the effective theory mass parameters fixed at Λ by the fundamental theory were hierarchically smaller than Λ itself. While this mechanism most probably cannot work in the Standard Model if the scale Λ is to be close to the Planck scale, we show that it can work in a minimal extension (Conformal Standard Model) proposed recently for a different implementation of conformal symmetry breaking.

scholarly journals PHASE TRANSITION COUPLINGS IN U(1) and SU(N) REGULARIZED GAUGE THEORIES

2001 ◽  
Vol 16 (24) ◽  
pp. 3989-4009 ◽  
Author(s):  
L. V. LAPERASHVILI ◽  
D. A. RYZHIKH ◽  
H. B. NIELSEN
Keyword(s):  
Phase Transition ◽  
Effective Potential ◽  
Gauge Theories ◽  
Planck Scale ◽  
Structure Constant ◽  
Coupling Constants ◽  
Fine Structure Constant ◽  
Multiple Point ◽  
Yang Mills ◽  
Loop Approximation

Using a two-loop approximation for β functions, we have considered the corresponding renormalization group improved effective potential in the dual Abelian Higgs model (DAHM) of scalar monopoles and calculated the phase transition (critical) couplings in U(1) and SU (N) regularized gauge theories. In contrast to our previous result α crit ≈0.17, obtained in the one-loop approximation with the DAHM effective potential (see Ref. 20), the critical value of the electric fine structure constant in the two-loop approximation, calculated in the present paper, is equal to α crit ≈0.208 and coincides with the lattice result for compact QED10: [Formula: see text]. Following the 't Hooft's idea of the "Abelization" of monopole vacuum in the Yang–Mills theories, we have obtained an estimation of the SU (N) triple point coupling constants, which is [Formula: see text]. This relation was used for the description of the Planck scale values of the inverse running constants [Formula: see text] (i= 1, 2, 3 correspond to U(1), SU(2) and SU(3) groups), according to the ideas of the multiple point model.16

scholarly journals Non-linear composition and infinite conformal symmetry of topologically non-trivial solutions in $$(3+1)$$-dimensional Yang–Mills theory

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Fabrizio Canfora
Keyword(s):  
Scalar Field ◽  
Charge Density ◽  
Topological Charge ◽  
Conformal Symmetry ◽  
Analytic Solutions ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Field Equations ◽  
Yang Mills ◽  
Non Linear

AbstractAn infinite-dimensional family of analytic solutions in pure SU(2) Yang–Mills theory at finite density in $$(3+1)$$ ( 3 + 1 ) dimensions is constructed. It is labelled by two integeres (p and q) as well as by a two-dimensional free massless scalar field. The gauge field depends on all the 4 coordinates (to keep alive the topological charge) but in such a way to reduce the (3+1)-dimensional Yang–Mills field equations to the field equation of a 2D free massless scalar field. For each p and q, both the on-shell action and the energy-density reduce to the action and Hamiltonian of the corresponding 2D CFT. The topological charge density associated to the non-Abelian Chern–Simons current is non-zero. It is possible to define a non-linear composition within this family as if these configurations were “Lego blocks”. The non-linear effects of Yang–Mills theory manifest themselves since the topological charge density of the composition of two solutions is not the sum of the charge densities of the components. This leads to an upper bound on the amplitudes in order for the topological charge density to be well-defined. This suggests that if the temperature and/or the energy is/are high enough, the topological density of these configurations is not well-defined anymore. Semiclassically, one can show that (depending on whether the topological charge is even or odd) some of the operators appearing in the 2D CFT should be quantized as Fermions (despite the Bosonic nature of the classical field).

scholarly journals TESTS OF LORENTZ AND CPT VIOLATION WITH MiniBooNE NEUTRINO OSCILLATION EXCESSES

2012 ◽  
Vol 27 (25) ◽  
pp. 1230024 ◽  
Author(s):  
TEPPEI KATORI
Keyword(s):  
Standard Model ◽  
Neutrino Oscillation ◽  
Lorentz Invariance ◽  
Planck Scale ◽  
Lorentz Violation ◽  
New Physics ◽  
Cpt Symmetry ◽  
Standard Model Extension ◽  
Sidereal Time ◽  
Short Baseline

Violation of Lorentz invariance and CPT symmetry is a predicted phenomenon of Planck-scale physics. Various types of data are analyzed to search for Lorentz violation under the Standard Model Extension (SME) framework, including neutrino oscillation data. MiniBooNE is a short-baseline neutrino oscillation experiment at Fermilab. The measured excesses from MiniBooNE cannot be reconciled within the neutrino Standard Model (νSM); thus it might be a signal of new physics, such as Lorentz violation. We have analyzed the sidereal time-dependence of MiniBooNE data for signals of the possible breakdown of Lorentz invariance in neutrinos. In this brief review, we introduce Lorentz violation, the neutrino sector of the SME and the analysis of short-baseline neutrino oscillation experiments. We then present the results of the search for Lorentz violation in MiniBooNE data. This review is based on the published result.

scholarly journals THE EXCEPTIONAL E8 GEOMETRY OF CLIFFORD (16) SUPERSPACE AND CONFORMAL GRAVITY YANG–MILLS GRAND UNIFICATION

2009 ◽  
Vol 06 (03) ◽  
pp. 385-417 ◽  
Author(s):  
CARLOS CASTRO PERELMAN
Keyword(s):  
Field Theory ◽  
Planck Scale ◽  
Gravitational Theory ◽  
Spin Connection ◽  
Conformal Gravity ◽  
Unified Field Theory ◽  
Yang Mills ◽  
Unified Field ◽  
Curved Slice ◽  
Symplectic Clifford Algebras

We continue to study the Chern–Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos–Lovelock Gravitational theory with a E8 Generalized Yang–Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E8 Geometry of the 256-dim slice of the 256 × 256-dimensional flat Clifford (16) space is explicitly constructed based on a spin connection [Formula: see text], that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 × 256 components of the vielbein field [Formula: see text], that gauge the nonabelian translations. Thus, in one-scoop, the vielbein [Formula: see text] encodes all of the 248 (nonabelian) E8 generators and 8 additional (abelian) translations associated with the vectorial parts of the generators of the diagonal subalgebra [Cl(8) ⊗ Cl(8)] diag ⊂ Cl(16). The generalized curvature, Ricci tensor, Ricci scalar, torsion, torsion vector and the Einstein–Hilbert–Cartan action is constructed. A preliminary analysis of how to construct a Clifford Superspace (that is far richer than ordinary superspace) based on orthogonal and symplectic Clifford algebras is presented. Finally, it is shown how an E8 ordinary Yang–Mills in 8D, after a sequence of symmetry breaking processes E8 → E7 → E6 → SO(8, 2), and performing a Kaluza–Klein–Batakis compactification on CP2, involving a nontrivial torsion, leads to a (Conformal) Gravity and Yang–Mills theory based on the Standard Model in 4D. The conclusion is devoted to explaining how Conformal (super) Gravity and (super) Yang–Mills theory in any dimension can be embedded into a (super) Clifford-algebra-valued gauge field theory.

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