Mass without mass from a berry–shifted SU(3) holonomy rotor

In this article*, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Sec.2), “it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms”; where in agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to fundamental laws of nature is as follows. First based on the assumption of rationality of D-momentum, by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford, and symmetric algebras) is derived. Then by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras) is derived uniquely as well. Each class of the derived general covariant field equations also includes a definite form of torsion field appeared as generator of the corresponding field’ invariant mass. In addition, it is shown that the (1+3)-dimensional cases of two classes of derived field equations represent a new general covariant massive formalism of bispinor fields of spin-2, and spin-1 particles, respectively. In fact, these uniquely determined bispinor fields represent a unique set of new generalized massive forms of the laws governing the fundamental forces of nature, including the Einstein (gravitational), Maxwell (electromagnetic) and Yang-Mills (nuclear) field equations. Moreover, it is also shown that the (1+2)-dimensional cases of two classes of these field equations represent a new general covariant massive formalism of bispinor fields of spin-3/2 and spin-1/2 particles, corresponding (asymptotically) to the Dirac and Rarita–Schwinger equations. As a particular consequence, it is shown that a certain massive formalism of general relativity – with a definite form of torsion field appeared originally as the generator of gravitational field’s invariant mass – is obtained only by first quantization (followed by a basic procedure of minimal coupling to space-time geometry) of a certain set of special relativistic algebraic matrix equations. In addition, in agreement with recent astronomical data, a new particular form of massive particle is identified (as the gauge boson of U(1) symmetry group) with invariant mass: m_γ ≈ 4.90571×10^-50 kg, which is generated by a definite coupled torsion field of the background space-time geometry. Moreover, based on the definite mathematical formalism of this axiomatic approach, along with the C, P and T symmetries (represented basically by the corresponding quantum operators) of the fundamentally derived field equations, it has been concluded that the universe could be realized solely with the (1+2) and (1+3)-dimensional space-times (where this conclusion, in particular, is based on the T-symmetry of these equations). It is shown that CPT is the only combined form of C, P, and T symmetries of interacting fields. In addition, on the basis of these discrete symmetries of derived field equations, it has been also shown that only left-handed particle fields (along with their complementary right-handed fields) could be coupled to the corresponding (any) source currents. Furthermore, it has been shown that the metric of background space-time is diagonalized for the uniquely derived fermion field equations (defined and expressed solely in (1+2)-dimensional space-time), where this property generates a certain set of additional symmetries corresponding uniquely to the "SU(2)_L⊗U(2)_R" symmetry group for spin-1/2 fermion fields (representing “1+3” generations of four fermions, including a group of eight leptons and a group of eight quarks), and also the "SU(2)_L⊗U(2)_R" and SU(3) gauge symmetry groups for spin-1 boson fields coupled to the spin-1/2 fermionic source currents. Hence, along with the known elementary particles, eight new elementary particles, including four new charge-less right-handed spin-1/2 fermions (including two leptons and two quarks), a spin-3/2 fermion, and also three new spin-1 (massive) bosons are predicted uniquely by this new mathematical axiomatic approach. As a particular result, based on the definite formulation of the derived Maxwell (and Yang-Mills) field equations, it has been also concluded that magnetic monopoles could not exist in nature.* *Note: "See also new published version of this article at: https://inspirehep.net/record/1387680/ ”. Comments: 90 Pages. A summary of a submitted and accepted research project (On "Foundations of Physics"), Ramin Zahedi, Japan, 2012 - 2015. This article has been invited and presented at the following international conferences: - The 2016 SIAM International Conference on Mathematical Aspects of Materials Science, Philadelphia, USA, 2016. (https://www.siam.org/meetings/ms16) - The 17th International Conference on Quantum Foundations: Quantum and Beyond, International Centre for Mathematical Modeling in Physics, Engineering and Cognitive Sciences (ICMM), Linnaeus University, Sweden, 2016. (https://lnu.se/en/qb/) -The 4th International Conference on New Frontiers in Physics, CERN Organized and Supported Conference (Europe), ICNFP-2015. (https://indico.cern.ch/e/icnfp2015/) - The 2016 International Conference on Algebraic Geometry and Mathematical Physics, University of Tromsø, Norway, 2016. (https://site.uit.no/) - The XXXVII Max Born International Symposium, International Conference on Non-commutative Geometry, Quantum Symmetries and Quantum Gravity (II), Wroclaw University, Poland, 2016. (http://ift.uni.wroc.pl/~mborn37/) - The 2016 GRavitational-wave Astronomy International Conference in Paris, Institute d‘Astrophysique de Paris (IAP), The University of Paris VI - Sorbonne University, CNRS, LERU, EUA, Paris, France, 'Supported by the European Union's 7th Framework Program: FP7/PEOPLE-2011-CIG,‘ 2016. (http://www.iap.fr/vie_scientifique/ateliers/GravitationalWave/2016/scripts/abstract.aspx) - The 22nd Internnational Australian Institute of Physics Congress (AIP), University of Queensland, Brisbane, Australia, 2016. (http://appc-aip2016.org.au) - The 21st International Conference on General Relativity and Gravitation, Columbia University, New York, USA, 2016. (http://www.gr21.org). External URLs (including preprints and earlier published versions of this research article): https://cds.cern.ch/record/1980381/ , https://inspirehep.net/record/1387680/, https://indico.cern.ch/event/344173/session/22/contribution/422/attachments/1140145/1646101/R.a.Zahedi--OnDiscretePhysics-Jan.2015-signed.pdf, http://eprints.lib.hokudai.ac.jp/dspace/handle/2115/59279/, https://core.ac.uk/display/41879427, http://www.gr21.org/GR21FullAbstractBooklet.pdf#section*.177, https://dx.doi.org/10.17605/OSF.IO/ZCHTP, https://dumas.ccsd.cnrs.fr/TDS-MACS/hal-01476703 , https://indico.cern.ch/event/344173/contribution/1740565/attachments/1140145/1726912/R.A.Zahedi--Forces.of.Nature.Laws-Jan.2015-signed.pdf , http://mts-ncomms.nature.com/ncomms_files/2017/07/10/00136200/00/136200_0_art_file_2445656_bsw9c4.pdf .

No coincidence of center percolation and deconfinement in SU(4) lattice gauge theory

We consider large Wilson loops with quarks in higher representations in SU(N) Yang-Mills theories. We consider representations with common N-ality and check whether the expectation value of the Wilson loop depends on the specific representation or only on the N-ality. In the framework of AdS/CFT we show that <W_R> = dim R exp -sigma_k A, namely that the string tension depends only on the N-ality k but the pre-exponent factor is representation dependent. The lattice strong coupling expansion yields an identical result at infinite N, but shows a representation dependence of the string tension at finite N, a result which we interpret as an artifact. In order to confirm the representation independence of the string tension we re-analyse results of lattice simulations involving operators with common N-ality in pure SU(N) Yang-Mills theory. We find that the picture of the representation-independence of the string tension is confirmed by the spectrum of excited states in the stringy sector, while the lowest-lying states seem to depend on the representation. We argue that this unexpected result is due to the insufficient distance of the static sources for the asymptotic behaviour to be visible and give an estimate of the distance above which a truly representation-independent spectrum should be observed.

The dependence of the Landau gauge two point gluon and ghost correlation\nfunctions on the lattice spacing and on the physical volume are investigated\nfor pure SU(3) Yang-Mills theory in four dimensions using lattice simulations.\nWe present data from very large lattices up to $128^4$ and for two lattice\nspacings $0.10$ fm and $0.06$ fm corresponding to volumes of $\\sim$ (13 fm)$^4$\nand $\\sim$ (8 fm)$^4$, respectively. Our results show that, for sufficiently\nlarge physical volumes, both propagators have a mild dependence on the lattice\nvolume. On the other hand, the gluon and ghost propagators change with the\nlattice spacing $a$ in the infrared region, with the gluon propagator having a\nstronger dependence on $a$ compared to the ghost propagator. In what concerns\nthe strong coupling constant $\\alpha_s (p^2)$, as defined from gluon and ghost\ntwo point functions, the simulations show a sizeable dependence on the lattice\nspacing for the infrared region and for momenta up to $\\sim 1$ GeV.\n

We are interested in a gauge invariant coupling between four-dimensional Yang–Mills field and a three-brane that can fluctuate into higher dimensions. For this we interpret the Yang–Mills theory as a higher dimensional bulk gravity theory with dynamics that is governed by the Einstein action, and with a metric tensor constructed from the gauge field in a manner that displays the original gauge symmetry as an isometry. The brane moves in this higher dimensional spacetime under the influence of its bulk gravity, with dynamics determined by the Nambu action. This introduces the desired interaction between the brane and the gauge field in a way that preserves the original gauge invariance as an isometry of the induced metric. After a prudent change of variables the result can be interpreted as a gauge invariant and massive vector field that propagates in the original spacetime . The presence of the brane becomes entirely invisible, expect for the mass.

We review work on the construction of Monopoles in higher dimensions. These are solutions to a particular class of models descending from Yang–Mills systems on even-dimensional bulk, with spheres as codimensions. The topological lower bounds on the Yang–Mills action translate into Bogomol'nyi lower bounds on the residual Yang–Mills–Higgs systems. Mostly, consideration is restricted to eight-dimensional bulk systems, but extension to the arbitrary case follows systematically. After presenting the monopoles, the corresponding dyons are also constructed. Finally, new Chern–Simons densities expressed in terms of Yang–Mills and Higgs fields are presented. These are defined in all dimensions, including in even-dimensional spacetimes. They are constructed by subjecting the dimensionally reduced Chern–Pontryagin densities to a further descent by two steps.

Recent experimental realizations of the lattice Schwinger model [Nature 587, 392 (2020) and Science 367, 1128 (2020)] open a door for quantum simulation of elementary particles and their interactions using ultracold atoms, in which the matter and gauge fields are constrained by a local U(1) gauge invariance known as the Gauss's law. Stimulated by such exciting progress, we propose a new scenario in simulating the lattice Schwinger model in a spin-1 Bose-Einstein condensate. It is shown that our model naturally contains an interaction of the matter fields which respects the U(1) gauge symmetry but has no counterpart in the conventional Schwinger model. In addition to the Z2-ordered phase identified in the previous work, this additional interaction leads to a new Z3-ordered phase. We map out a rich phase diagram and identify that the continuous phase transitions from the disordered to the Z2-ordered and the Z3-ordered phases belong to the Ising and the 3-state Potts universality classes, respectively. Furthermore, the two ordered phases each possess a set of quantum scars which give rise to anomalous quantum dynamics when quenched to a special point in the phase diagram. Our proposal provides a novel platform for extracting emergent physics in cold-atom-based quantum simulators with gauge symmetries.

In this chapter we are concerned with other electrodynamic theories which show new features, not present in four-dimensional spinor QED. The new feature in scalar QED is the derivative coupling between the scalar field and the vector potential. It has important consequences for gauge invariance, in particular, the interaction gets modified by gauge invariance. Such derivative couplings also occur in Yang-Mills theories, and the same implications of gauge invariance appear here. This is briefly discussed in the Epilogue. The axial anomalies, that we describe next, provide an important example where gauge invariance partially breaks down. These anomalies also occur in the standard electro-weak theory and must be compensated there. This implies the lepton-quark duality, which means that to each lepton family (e, μ, τ) there must exist a corresponding quark family. Finally, if QED in two space plus one time dimensions is considered, the vacuum polarization shows unusual behaviour. This has the surprising consequence that the photon becomes massive. These examples illustrate how rich QED really is.

Yang-Mills fields in the temporal gauge are transformed into pure gauge variables and gauge-invariant first integrals of Gauss's-law differential equations. It is observed that the Schr\"odinger equation becomes separable in the new variable system.

In the lattice work by Miller and in the work by Zwanziger a linear growth of the trace anomaly for high temperatures was found in pure SU(2) and SU(3) Yang-Mills theories. While future numerical work is needed to confirm or to rule out the linear growth, the aforementioned results point to the remarkable property that the corresponding systems are strongly interacting even at high temperatures. We show that within an analytical approach to Yang-Mills thermodynamics this linear rise is obtained and is directly connected to the presence of a temperature-dependent ground state, which describes (part of) the nonperturbative nature of the Yang-Mills system. Our predictions are in approximate agreement with Miller and Zwanziger.

The gauge structure of the four dimensional effective theory (4DET) arising from a pure Yang-Mills theory in five dimensions compactified on the orbifold $S^1/Z_2$ is reexamined on the basis of the BRST symmetry. The two scenarios that can arise are analyzed: if the gauge parameters propagate in the bulk, the excited Kaluza-Klein (KK) modes are gauge fields, but they are matter vector fields if these parameters are confined in the 3-brane. In the former case, it is shown that the 4DET is gauge invariant only if the compactification is carried out by using curvatures instead of gauge fields as fundamental objects. It is shown that the 4DET is governed by two types of gauge transformations, one determined by the KK zero modes of the gauge parameters and the other by the excited KK modes. The Dirac's method and the proper solution of the master equation are employed to show that the theory is subject to first class constraints. A gauge-fixing procedure to quantize the KK modes, that is covariant under the first type of gauge transformations, is introduced. The ghost sector induced by these gauge-fixing functions is derived on the basis of the BRST formalism. The effective quantum Lagrangian that links the interactions between light physics and heavy physics is presented. Concerning the radiative corrections of the excited KK modes on the light Green functions, the predictive character of this Lagrangian is stressed. In the case of the gauge parameters confined to the 3-brane, the known result in the literature is reproduced with some minor variants, although it is emphasized that the excited KK modes are not gauge fields, but matter fields that transform under the adjoint representation of $SU_4(N)$. The Dirac's method is employed to show that this theory is subject to both first and second class constraints.

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model.The gauge invariant version of the chiral Schwinger model for $a=2$ has a massive field with identical mass however gauge invariant version obtained here does not map on to that.

In this paper we present a renormalizability proof for spontaneously broken SU(2) gauge theory. It is based on Flow Equations, i.e. on the Wilson renormalization group adapted to perturbation theory. The power counting part of the proof, which is conceptually and technically simple, follows the same lines as that for any other renormalizable theory. The main difficulty stems from the fact that the regularization violates gauge invariance. We prove that there exists a class of renormalization conditions such that the renormalized Green functions satisfy the Slavnov–Taylor identities of SU(2) Yang–Mills theory on which the gauge invariance of the renormalized theory is based.

The free field equations for particles with spin are invariant under a group SL(2, c) whose transformations correspond to changes of representation of the twocomponent spinor algebra. The generalization of the equations which extends this invariance to a guage invariance in the Yang–Mills sense necessitates the introduction of auxiliary fields (which are also necessary to maintain Lorentz covariance). These fields can be interpreted as the potentials of a spin-2 field, just as the auxiliary fields for the charge gauge group are the potentials of a spin-l field (electromagnetism); this spin-2 field is then self-interacting. The Bargmann–Wigner formulation of the linear spin-2 field, when modified by the proposed self-interaction, yields a non-linear theory of a spin-2 field which is shown to be identical with Einstein's gravitational theory. With this interpretation the auxiliary fields take on an extra role of Yang–Mills field for the general coordinate transformation group – that is, they are the components of the affine connexion.

The gauge symmetry principles of the Yang–Mills field of 1954 provide the solid rock foundation for the Standard Model of particle physics. To give masses to the quarks and leptons, however, SM calls on the solitary Higgs field using a set of mysterious complex Yukawa coupling matrices. We enrich the SM by reducing the Yukawa coupling matrices to a single Yukawa coupling constant, and endowing it with a family of Higgs fields that are degenerate in mass. The recent experimental discovery of the Higgs resonance at 125.09 ± 0.21 GeV does not preclude this possibility. Instead, it presents an opportunity to explore the interference effects in background events at the LHC. We present a study based on the maximally symmetric Higgs potential in a leading hierarchy scenario.