CPT Transformations Research Articles

Antimatter Gravity and the Results of the ALPHA‐g Experiment

AbstractBy combining general relativity and CPT symmetry, the theory of CPT gravity predicts gravitational repulsion between matter and CPT‐transformed matter, i.e., antimatter inhabiting an inverted space‐time. Such repulsive gravity turned out to be an excellent candidate for explaining the accelerated expansion of the Universe, without the need for dark energy. The recent results of the ALPHA‐g experiment, which show gravitational attraction between antihydrogen atoms and the Earth, seem to undermine this success in the cosmological field. Analyzing the above theory, two solutions are found that can be consistent with the experimental results, while preserving the large‐scale gravitational repulsion. The first highlights how repulsive gravity can be the result of the interaction with an inverted space‐time, but occupied by matter and not antimatter, and therefore the antimatter present in our space‐time has no reason to exhibit gravitational repulsion. The second retains the original CPT transformation, resulting in repulsive gravity between matter and antimatter, but with the caveat that antimatter immersed in our space‐time cannot exhibit the PT transformation which is the cause of the repulsion. Finally, it is shown that, in a Newtonian approximation of the geodesic equation, time reversal is not a necessary operation for repulsive gravity, therefore opening the possibility of an expanding cosmos with a single time direction.

Gauge CPT: A review and use in constructing new affine connections

In this paper, we review the gauge theory of CPT transformations. Even though it may seem absurd to entertain the notion of gauging a discrete symmetry because there are no continuous parameters, we show otherwise via a “back door”. We also make use of the components of the new gauge field [Formula: see text] which are an extension of the metric spin connection to construct various affine connections.

A brief tour of gauge CPT

We outline the gauge theory of CPT transformations. Gauge CPT provides an alternative to the dark matter hypothesis by unveiling a natural extension of general relativity. Additionally, the new dynamical degrees of freedom revealed by gauge CPT should be essential for any approach to quantum gravity. Even though it may seem absurd to entertain the notion of gauging a discrete symmetry because there are no continuous parameters, we show otherwise via a “back door”.

On Quantum Entropy.

Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of its observables; it trivially vanishes for pure quantum states. We propose a quantum entropy that quantifies the randomness of a pure quantum state via a conjugate pair of observables/operators forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under canonical transformations and under CPT transformations, and its minimum has been established by the entropic uncertainty principle. We expand the entropy to also include mixed states. We show that the entropy is monotonically increasing during a time evolution of coherent states under a Dirac Hamiltonian. However, in a mathematical scenario, when two fermions come closer to each other, each evolving as a coherent state, the total system’s entropy oscillates due to the increasing spatial entanglement. We hypothesize an entropy law governing physical systems whereby the entropy of a closed system never decreases, implying a time arrow for particle physics. We then explore the possibility that as the oscillations of the entropy must by the law be barred in quantum physics, potential entropy oscillations trigger annihilation and creation of particles.

What Is the Universe Ultimately Made of?

As the ultimate building blocks of the universe, the limit structureless quark u∞ and its anti-quark are considered at the infinite sublayer level of the quark model. Then CP is violated in the doublet of u∞ and u∞CP quarks to account for the asymmetry of the number of particles and anti-particles. This CP violation is explained by a SU(2) noncommutative geometry. The second, third and fourth generation quarks are considered only as the excited states of the first generation u∞ and u∞CP quarks. The fourth generation quarks are derived from both CPT transformation and the SU(2)L×U(1) gauge theory. The dark matter, quarks, leptons, gauge bosons and Higgs bosons are composed of only the u∞ and u∞CP quarks and the cosmological constant in Einstein’s field equation is also derived from the Higgs potential. Thus, the limit particle u∞ and its anti-particle u∞CP are the ultimate particles of the universe and produced thermally in the hot early universe of the Big Bang.

Quaternionic Approach to Dual Magnetohydrodynamics of Dyonic Cold Plasma

The dual magnetohydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual fields equations, namely, the hydroelectric and hydromagnetic fields equations which are an analogous to the generalized Lamb vector field and vorticity field equations of dyonic cold plasma fluid. Further, we derive the quaternionic Dirac-Maxwell equations for dual magnetohydrodynamics of dyonic cold plasma. We also obtain the quaternionic dual continuity equations that describe the transport of dyonic fluid. Finally, we establish an analogy of Alfven wave equation which may generate from the flow of magnetic monopoles in the dyonic field of cold plasma. The present quaternionic formulation for dyonic cold plasma is well invariant under the duality, Lorentz, and CPT transformations.

Measurement of the mass difference between top quark and antiquark in pp collisions at [formula omitted

The invariance of the standard model (SM) under the CPT transformation predicts equality of particle and antiparticle masses. This prediction is tested by measuring the mass difference between the top quark and antiquark (Δmt=mt−mt‾) that are produced in pp collisions at a center-of-mass energy of 8 TeV, using events with a muon or an electron and at least four jets in the final state. The analysis is based on data corresponding to an integrated luminosity of 19.6 fb−1collected by the CMS experiment at the LHC, and yields a value of Δmt=−0.15±0.19(stat)±0.09(syst) GeV, which is consistent with the SM expectation. This result is significantly more precise than previously reported measurements.

On the CPT theorem

We provide a careful development and rigorous proof of the CPT theorem within the framework of mainstream (Lagrangian) quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches in the mainstream approach. We construct the CPT transformation for a general field directly, without appealing to the enumerative classification of representations, and in a manner that is clearly related to the requirements of our proof. Our approach applies equally in Minkowski spacetimes of any dimension at least three, and is in principle neutral between classical and quantum field theories: the quantum CPT theorem has a natural classical analogue. The key mathematical tool is that of complexification; this tool is central to the existing axiomatic proofs, but plays no overt role in the usual mainstream approaches to CPT.

SYMMETRY PROPERTIES OF THE EXACT EM RADIATION-REACTION EQUATION FOR CLASSICAL EXTENDED PARTICLES AND ANTIPARTICLES

Based on recent theoretical developments (Cremaschini and Tessarotto, 2011–2013), in this paper the issue is addressed of the first-principle construction of the nonlocal relativistic radiation-reaction (RR) equation for classical spherical-shell, finite-size particles and antiparticles. This is achieved invoking the axioms of Classical Electrodynamics by means of the Hamilton variational principle. In connection with this, the Lagrangian conservation laws, together with the possible existence of adiabatic invariants, and the transformation laws of the RR equation with respect to CPT and time-reversal transformations are investigated. The latter properties make possible the parametrization of the RR equations, holding respectively for particles and antiparticles of this type, in terms of the same coordinate time t and the investigation of the qualitative properties of their solutions. In particular, in both cases the RR self-force is found to have the same signature, which implies that the dynamics of classical finite-size antiparticles is equivalent to that of classical extended particles of opposite charge. Therefore, in the framework of Classical Mechanics, a distinction between particles and antiparticles cannot be made based solely on the electromagnetic interactions associated with electromagnetic RR phenomena. As a basic application of the theory, the Lagrangian conservation laws and symmetry properties for the Hamiltonian asymptotic approximations of the exact RR equation are also addressed.

T and CPT symmetries in entangled neutral meson systems

Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-independent separate measurements of the three CP, T and CPT symmetry violations for transitions involving the decay of the neutral meson systems in B- and Φ-factories. It makes use of the quantum-mechanical entanglement only, for which the individual state of each neutral meson is not defined before the decay of its orthogonal partner. The final proof of the independence of the three asymmetries is that no other theoretical ingredient is involved and that the event sample corresponding to each case is different from the other two. The experimental analysis for the measurements of these three asymmetries as function of the time interval Δt > 0 between the first and second decays is discussed, as well as the significance of the expected results. In particular, one may advance a first observation of true, direct, evidence of Time-Reserval-Violation in B-factories by many standard deviations from zero, without any reference to, and independent of, CP-Violation.In some quantum gravity framework the CPT-transformation is ill-defined, so there is a resulting loss of particle-antiparticle identity. This mechanism induces a breaking of the EPR correlation in the entanglement imposed by Bose statistics to the neutral meson system, the so-called ω-effect. I present results and prospects for the ω-parameter in the correlated neutral meson-antimeson states.

NEUTRINO ASYMMETRY AROUND BLACK HOLES: NEUTRINOS INTERACT WITH GRAVITY

Propagation of fermions in curved spacetime generates gravitational interaction due to coupling of its spin with spacetime curvature connection. This gravitational interaction, which is an axial-four-vector multiplied by a four-gravitational vector potential, appears as a CPT violating term in the Lagrangian which generates an opposite sign and thus an asymmetry between the left-handed and the right-handed partners under the CPT transformation. In the case of neutrinos, this property can generate neutrino asymmetry in the Universe. If the background metric is of the rotating black hole, i.e. the Kerr geometry, this interaction for the neutrino is nonzero. Therefore the dispersion energy relation for the neutrino and its anti-neutrino are different which gives rise to the difference in their number densities and neutrino asymmetry in the Universe in addition to the known relic asymmetry.

Linear Transformation Theory of Quantum Field Operators and Its Applications**The project supported by the Youth Sci-Tech “Qimingxing” Program of Shanghai, Foundation for University Key Teacher of Ministry of Education and Youth Science Foundation of Shanghai Higher Education

We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.

Interaction of a spin-1/2 particle with an electromagnetic field

An equation for the action of a spin-1/2 particle is proposed. The proposed action results in a second-order differential equation for the bispinor wavefunction of the particle. The obtained equation is compared with the Dirac equation. It is shown that all of the solutions of the Dirac equation satisfy the obtained equation. However, among the solutions of the second-order differential equation are solutions not satisfying the Dirac equation. The equation for the current density four-vector is derived. It is shown that the CPT transformation properties of the obtained current density four-vector are qualitatively different from that derived from those of the Dirac equation. The solution of the proposed equation for the problem of electron motion in the Coulomb field is found in analytically tractable form. The calculated spectrum is different from that described by the well-known Sommerfeld formula of the Dirac theory. The predicted spectrum includes the hyperfine structure which is doublet for the levels with the zero angular momentum and triplet for the levels with the non-zero orbital momentum. Analytically tractable solutions of the proposed equation are also found for the problems of electron motion in a uniform magnetic field, and in a superposition of Coulomb and uniform magnetic fields.

A gauge theory of CPT transformations to first order

The CPT symmetry is made local for the Dirac field and an analogous local symmetry is proposed for curved spacetime. A nontrivial, infinitesimal variation of the Dirac action is thus induced. It is shown that the metric spin connection of general relativity cannot accommodate this symmetry. A new gauge field is therefore introduced, which turns out to be a real pseudovector field, and its equations of motion are derived.

CPTanomaly in two-dimensional chiralU(1)gauge theories

The CPT anomaly, which was first seen in perturbation theory for certain four-dimensional chiral gauge theories, is also present in the exact result for a class of two-dimensional chiral $U(1)$ gauge theories on the torus. Specifically, the chiral determinant for periodic fermion fields changes sign under a CPT transformation of the background gauge field. There is, in fact, an anomaly of Lorentz invariance, which allows for the CPT theorem to be circumvented.

A five-dimensional form of the Dirac equation

A Dirac equation in a covariant form with respect to proper orthochronous rotations in (4 + 1)-dimensional pseudo-orthogonal space, i.e. Minkowski space extended by one real dimension is introduced. It contains a five-vector potential with a non-electromagnetic fifth component. The invariance of this equation under the CPT transformation is conditioned by the assumption that the real fifth coordinate changes its sign under charge conjugation, and that it simultaneously changes its sign either under time reversal or under space inversion. The energy levels of an electron under the simultaneous action of Coulomb and central gravitational fields are determined. To this end, (1) new eigenspinors of the total angular momentum operator are derived, with non-zero entries in the first and fourth or in the second and third row of the column matrix and (2) a scalar function is constructed from doubly-periodic Jacobian elliptic functions which, in the limit of the vanishing modulus of the elliptic functions, replaces the function exp(i t) in the stationary-state solutions. The iterated five-dimensional equation contains the ten components of the antisymmetric field tensor. It also contains a term determining the potential energy operator of electron spin density in a non-electromagnetic field. The Pauli equation is derived from the five-dimensional equation, with the transformational characteristics of the original equation. It contains a spin-orbit coupling term depending on the non-electromagnetic potential.

Higgs as gauge fields on discrete groups and Standard Models for electroweak and electroweak-strong interactions

We complete the construction of the gauge theory on discrete groups coupled to fermions in the spirit of non-commutative geometry. We show that a simple Higgs field is such a gauge field with respect toZ2-gauge symmetry overM4 and the Yukawa coupling between Higgs and fermions is automatically introduced via minimum coupling principle. TheZ2-symmetry is taken to be Θ={e, r=(CPT)2}, a sub-symmetry of the CPT transformations. The Weinberg-Salam model for the electroweak interaction as well as the Standard Model for the electroweak-strong interaction are reformulated in detail.

The restricted CPT gauge symmetry and the Weinberg-Salam model

By means of an approach to the generalized gauge theory on discrete groups we take the CPT transformations as a gauge group with a CPT transformation as a single element and reformulate the Weinberg-Salam model with the Higgs being a gauge field with respect to this restricted CPT gauged symmetry.

Representations of the full Lorentz group in quantum field theory

Various representations of the full Lorentz group are possible since the charge conjugation may be included into the realization of the parts of the group disjoint from the proper Lorentz transformations. Due to the antilinearity of charge conjugation in quantum mechanics (QM) and linearity in quantum field theory (QFT), these realizations differ in QM and QFT. Based on the observation that sign problems can be solved in relativistic quantum mechanics, it is shown that the second quantization of antiparticles can be modified to achieve consistency of QFT with QM. Modifications of the Wightman axioms are presented from which the existence of a unitary CPT transformation is derived.

The invariance of classical electromagnetism under charge conjugation, parity and time reversal (CPT) transformations

The invariance of classical electromagnetism under CPT is studied by considering the motion of a charged particle in electric and magnetic fields. Applying CPT transformations to various physical quantities and noting that the motion still behaves physically, the author demonstrates invariance.