Quaternion Quantum Mechanics as the description of tachyons and quarks

Physics is not symmetric with respect to time and space. To obtain symmetry between space and time, it is necessary to consider the new part of physics–the space-like physics in which the evolution takes place in space and the state of system is defined on the time axis. It is shown that the corresponding Quantum Mechanics must be based on the field of quaternions instead of the field of complex numbers. Equations analogical to the usual electrodynamics are found. In these equations the Yang-Mills field plays the role of the photon field. Then the corresponding hypothetical particles are interpreted as quarks. In this interpretation the symmetry between space and time is connected with the quark-lepton symmetry.     

Elementary particles as higher-dimensional tachyons

Elementary particles are described as higher-dimensional tachyonic modes. Their electromagnetic inertial mass would not match the gravitational mass unless their scalar hypercharge vanishes. The corresponding unified geometry surrounding an elementary electric monopole is extracted. Remarkably, the ingoing five-dimensional geodetic lines, associated with like-sign charged test particles, cannot classically penetrate the finite three-dimensional spherical core on which the extra-dimensional circle shrinks to a point.     

Farewell to tachyons?

It is shown that in addition to the usual difficulties related to causality, the theory of superluminal particles also exhibits paradoxical symmetry violations. In the second part of the paper a conventional paradox is revisited: causality violations at the macroscopic level follow from simple statistical arguments.     

Strings, tachyons and deconfinement

We argue that the tachyons which exist in some string models are a signal of deconfinement. We compare the deconfinement temperature obtained from Monte Carlo calculations with some strings models.     

Rest frames for tachyons and photons

A formalism is developed which admits particles faster than light and reference frames faster than light and as fast as light. It is fully consistent with the physical principles of special relativity. The necessity of introducing imaginary quantities does not arise. It does not encounter any difficulties with the principle of causality if it is reasonably interpreted.Dedicated to Prof. E. C. G. Sudarshan, in honor of his receipt of the Padmabushan Award.     

Barrier penetration as model for tachyons

Transmission of electromagnetic waves across an optically less-dense layer is proposed as a model for tachyons. Supercritical and subcritical incidence corresponds to tachyonic and bradyonic signals, respectively.     

Response to Kowalczyński about tachyons

An answer and brief comment are given to a paper about tachyons of Kowalczyński.     

Comments on “Farewell to tachyons?”

We comment on the previous paper by L. Basano. In particular, we show that its Section 2 is kinematically incorrect (the dynamics of a two-body interaction through tachyon exchange, incidentally, has already been thoroughly expounded in one paper of ours). Its Section 1 is simply a rather subjective introduction. As to its Section 3, containing indeed interesting problems, we again briefly refer to our earlier work. Our conclusions are still in favor of “au revoir to tachyons!,” even if it is known that inside our cosmos tachyons are more likely to have a role in physics (e.g., in elementary particle and black-hole physics) as “exchanged objects” rather than as “asymptotically free” objects.     

Magnetic monopoles and tachyons in special relativity

The mere special relativity does not explicitly predict existence of (sub-luminal) monopoles, but on the contrary explicitly predicts existence of super-luminal (tachyon) monopoles, with magnetic charge about 100 times less than usually assumed. This fact is relevant also at the light of current experiments looking for magnetic poles.     

Relativistic rigid particles: Classical tachyons and quantum anomalies

Causal rigid particles whose action includes anarbitrary dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, includingcausal tachyonic ones. The Hamiltonian formulation is developed in detail except for one degenerate situation for which only partial results are given and requiring a separate analysis. However, for otherwise generic rigid particles, the precise specification of Hamiltonian gauge symmetries is obtained with in particular the identification of the Teichmüller and modular spaces for these systems. Finally, canonical quantisation of the generic case is performed paying special attention to the phase space restriction due to causal propagation. A mixed Lorenz-gravitational anomaly is found in the commutator of Lorentz boosts with world-line reparametrisations. The subspace of gauge invariant physical states is therefore not invariant under Lorentz transformations. Consequences for rigid strings and membranes are also discussed.     

How to recover causality in special relativity for tachyons

In this paper we explain why and how tachyons do not imply any causality violation within relativistic theories. Particular emphasis is given to the role of the Stückelberg-Feynman reinterpretation principle, both in ordinary physics and in tachyon physics.Work partially supported by MPI (ex-art. 286) and by CNR under contract no. 75/00442.02.     

Do tachyons produce an unacceptable gravitational field?

The geodesics and the curvature of a metric representing an isolated tachyon are investigated. It is argued that the properties are unphysical and inconsistent with observation, thus providing further evidence against the existence of tachyons.     

A comment on fermionic tachyons and poincaré representations

We extend Wigner's work on the wave equations for integer-spin particles to the spinorial case. A recent suggestion that the neutrino might be a fermionic tachyon is examined. We point out that a four-component Dirac equation cannot describe a fermionic tachyon.     

The relativistic semi-group,Lorentz group,and tachyons. I

It is claimed that the current interest of tachyons and some of their unusual properties may be the result of an insufficient mathematical formalism based on Lorentz groups. The introduction of tachyons requires not only a generalization of the principle of causality, but also an extension of the principle of relativistic invariance. A method is proposed to remove a number of problematic cases in the treatment of tachyons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 85–88, May, 1976.The author wishes to express his appreciation to D. D. Ivanenko for consideration and constructive criticism.     

Vacuum instability and tachyons: Comments on a paper by Zeldovich

We show that vacuum instabilities possibly arising because of tachyons do not contradict any experimental evidence, and therefore that no objection against tachyon existence can be found even on this ground.     

The scattering amplitude for four off-shell tachyons from functional integrals

We use functional integral techniques to calculate the scattering amplitude for four open off-shell tachyons in Witten's string field theory and show that the residues of the first three poles agree with those obtained using oscillator methods.     

Relativistic semigroup,the lorentz group,and tachyons. IV

The algebraic and topological properties of the relativistic semigroup are discussed. Its probability-theoretical features establish that the relativistic semigroup belongs to the type of complex Markov structures. From the functional point of view, the relativistic semigroup is a compact Lie semigroup which is contracting in partial spaces. Principles of measurability, observability, and stochasticity are formulated, and these lead to a space-time structure of complex Markov kind. Thus, a certain probability-theoretical gnosiology is also possible in the theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 55–58, August, 1977.I thank D. D. Ivanenko for valuable advice and numerous discussions.