Covariant quantum field theory of tachyons (2308.00450v2)

Abstract: Three major misconceptions concerning quantized tachyon fields: the energy spectrum unbounded from below, the frame-dependent and unstable vacuum state, and the non-covariant commutation rules, are shown to be a result of misrepresenting the Lorentz group in a too small Hilbert space. By doubling this space we establish an explicitly covariant framework that allows for the proper quantization of the tachyon fields eliminating all of these issues. Our scheme that is derived to maintain the relativistic covariance also singles out the two-state formalism developed by Aharonov et al. [1] as a preferred interpretation of the quantum theory.

• The paper establishes a twin space formalism that enables Lorentz covariant quantization of tachyon fields.
• It resolves longstanding challenges such as an unbounded energy spectrum, unstable vacuum states, and non-covariant commutation rules.
• This framework opens new avenues for integrating tachyon fields into modern theories, with implications for Higgs physics and quantum gravity.

Covariant Quantum Field Theory of Tachyons

The paper "Covariant quantum field theory of tachyons" addresses substantial misconceptions regarding the quantization of tachyon fields within the framework of quantum field theory (QFT). The paper focuses on overcoming three persistent issues: an unbounded energy spectrum, frame-dependent and unstable vacuum states, and non-covariant commutation rules under Lorentz transformations. This analysis, performed by Paczos et al., reveals that these challenges stem from an inadequate representation of the Lorentz group in a limited Hilbert space. By proposing an extension to a twin space constructed as the tensor product of the standard Fock space with its dual, this paper establishes a new, covariant framework for properly quantizing tachyon fields.

Overview and Approach

The theoretical foundation primarily pivots on redefining the role of Lorentz group representations in the context of tachyons. Conventional representations in a single Hilbert space, suitable for subluminal particles, fall short for tachyons because positive-energy states in one frame can be transformed into negative-energy states in another through Lorentz boosts. To address this, the authors suggest representation within the extended, twin space ${\cal F}\otimes{\cal F}^\star$, maintaining both input (Fock) and output (its dual) states invariant under these transformations.

The focal point of their formulation is a novel application of the two-vector formalism in quantum mechanics, which originates from the works of Aharonov et al. on time symmetry in quantum processes. By conceptualizing twin space frameworks—infusing traditional 'in' and 'out' states with dual nature—the research guarantees covariance and stability across different inertial frames. The field operator, according to this proposal, is constructed from contributions of both the Fock space and its dual, thus ensuring relativity as well as preservation of commutation relations.

Strong Numerical Results and Claims

A significant claim made in the paper is the successful resolution of past failures to create a consistent, covariant tachyonic QFT, which had been encumbered by logical and mathematical inconsistencies. By maintaining a covariance-preserving twin space, the paper resolves the challenges described by earlier quantum mechanical attempts proposed by Arons, Sudarshan, and others, such as the lack of a consistent vacuum or unbounded energy spectrums, which previous methods couldn't successfully negate.

Practical and Theoretical Implications

The implications of successfully quantizing tachyon fields are twofold. Practically, this advancement revives the theoretical consideration of tachyons, which have been sidelined in high-energy physics due to their theoretical ambiguities. By presenting a stable and covariant framework, new dialogues around their possible integration into modern physical theories, such as those accommodating neutrino behaviors or in understanding spontaneous symmetry breaking in Higgs physics, may flourish.

Theoretically, the paper indicates a potential unification with broader interpretations of quantum mechanics, possibly relaxing incomplete descriptions tied to locality or time irreversibility. Moreover, through a connection with generalized two-state vectors, this scheme potentially illuminates issues in quantum gravity or spacetime quantization, as the extended Hilbert space model might more fundamentally interact with quantum-classical transition studies or gravitational field theories.

Future Developments

The authors recognize the necessity for further investigations to deploy this formalism within superluminal frames naturally. Additionally, exploring the interaction of tachyons with known particles, such as Higgs bosons, within the constructed framework can provide further insights into phase transitions and other high-energy processes. The extension to possible sectors of CP violation and baryogenesis processes during the cosmic inflation, particularly in extended Higgs scenarios, beckons extensive research.

In summary, the paper advances the understanding of tachyon quantization by setting a foundational stone that melds relativistic invariance with quantum symmetry. Moving forward, the task lies in leveraging this theory not only within theoretical physics but also in expanding practical experiments designed to conclusively investigate the existence and implications of tachyons.