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Cheng-Yang Lee

Publications and source records attributed to Cheng-Yang Lee.

At least 19 recordsLinked to original sources
arXiv2026

SUSY meets pseudo-Hermiticity

In this work, we construct the simplest pseudo-Hermitian quantum field theory that is supersymmetric. This is the pseudo-Hermitian Wess-Zumino model in the sense that it contains a pair of symplectic fermions (anti-commuting scalar fields) that satisfy the Klein-Gordon equation and a spin-half boson that satisfies the Dirac equation. The conventional spin-statistics theorem is circumvented through the use of pseudo-Hermitian conjugation to define field adjoints. To make the supersymmetry manifest, we formulate the pseudo-Hermitian Wess-Zumino model using the superfield formalism. These superfields are Grassmann-odd so it is not possible to construct non-vanishing cubic interactions using only these superfields. We show that this problem can be resolved by coupling the pseudo-Hermitian Wess-Zumino model with the Hermitian Wess-Zumino model while preserving supersymmetry.

hep-th↗
arXiv2025

Pseudo-Hermitian QFT: relativistic scattering and symmetry structure

Unitarity is a cornerstone of quantum theory, ensuring the conservation of probability and information. Although non-Hermitian Hamiltonians are typically associated with open or dissipative systems, pseudo-Hermitian quantum mechanics shows that real spectra and unitary evolution can still emerge through a suitably defined inner product. Motivated by this insight, we extend the pseudo-Hermitian framework to relativistic quantum field theory and construct a consistent formulation of scattering processes. A novel structural feature of this theory is the presence of distinct metric operators for the in and out sectors, connected through a nontrivial metric projector that guarantees global probability conservation under pseudo-unitary time evolution. We further develop a general symmetry formalism, showing that each symmetry generally corresponds to two pseudo-unitary operators associated with the in and out metrics, respectively. Within this framework, the scattering matrix admits a perturbative expansion through the Dyson series and remains Lorentz invariant and unitary, remarkably in complete agreement with the conventional Hermitian case. The fundamental CPT theorem is also shown to hold. Our results provide a rigorous foundation for interacting pseudo-Hermitian quantum field theories and open new directions for exploring their possible physical implications beyond the standard Hermitian paradigm.

hep-th↗
arXiv2025

The anomalous spin-statistics connection arising from pseudo-Hermiticity

We establish a new spin-statistics theorem for a class of free pseudo-Hermitian quantum field theories whose particles furnish unitary irreducible representations of the Poincar\'{e} group. In this framework, free pseudo-Hermitian fields with integer spin exhibit fermionic statistics, whereas those with half-integer spin exhibit bosonic statistics, opposite to the conventional case. This reversal arises from defining canonical field operators using pseudo-Hermitian conjugation rather than Hermitian conjugation, thereby circumventing the conventional spin-statistics theorem. The free fields retain locality, Lorentz covariance, and unitary evolution. However, interactions may violate unitarity due to the intrinsically non-Hermitian nature of the full Hamiltonian. We discuss potential resolutions to restore unitarity in interacting theories.

hep-th↗
arXiv2025

Wigner multiplets in QFT: from Wigner degeneracy to Elko fields

We establish the theoretical foundation of the Wigner superposition field, a quantum field framework for spin-1/2 fermions that exhibit a Wigner doublet -- a discrete quantum number arising from nontrivial representations of the extended Poincar\'{e} group. In contrast to the previously developed doublet formalism, which treats the Wigner degeneracy as a superficial label, the superposition formalism encodes it directly into the structure of a unified field via a coherent superposition of degenerate spinor fields. By imposing the Lorentz covariance, causality, and canonical quantization, we derive nontrivial constraints on the field configuration, which uniquely identify the Elko field as the consistent realization of the Wigner superposition field. Our analysis further clarifies that although the Elko field is a spinor field, it possesses mass dimension one and obeys the Klein-Gordon rather than the Dirac kinematics. Moreover, we explore the general Elko representation through basis redefinitions, showing that certain traditional properties, such as being eigenspinors of charge conjugation, are artifacts of specific basis choices rather than intrinsic features. Finally, we discuss the physical implications of Elko as a dark matter (DM) candidate. This work lays the foundation for a systematic reformulation of Elko interactions and its phenomenology as a viable component of DM.

hep-th↗
arXiv2025

Wigner multiplets in QFT: dark sector and CPT-violating scenarios

The classification of elementary particles based on unitary irreducible representations of the Poincare group has been a cornerstone of modern Quantum Field Theory (QFT). While the Standard Model (SM) does not inherently include Dark Matter (DM), any fundamental DM candidate should still conform to this classification or its extensions. Beyond the standard representations, Wigner introduced a class of nontrivial states characterized by an additional discrete degree of freedom, known as the Wigner degeneracy. We systematically investigate the QFT of such Wigner degenerate multiplets, particularly focusing on the massive spin-1/2 case. We construct a theoretical framework where the two-fold Wigner spinor fields, $\psi_{\pm\frac{1}{2}}(x)$, form a doublet representation. We analyze their transformation properties under discrete symmetries (C, P, and T), revealing novel mixing effects due to Wigner degeneracy and an emergent accidental U(2) global symmetry. Furthermore, we explore their Yukawa and gauge interactions, demonstrating that such interactions generally break the CPT symmetry. However, we derive conditions for the CPT conservation and discuss potential phenomenological consequences beyond the SM. These results provide new insights into the possible role of Wigner-degenerate states in fundamental physics, particularly in the dark sector.

hep-ph↗
arXiv2024

Correlators for pseudo Hermitian systems

Pseudo-Hermitian system is a class of non-Hermitian system with Hamiltonian satisfying the condition $\eta^{-1}H^\dagger\eta=H$. We develop the in-in and Schwinger Keldysh formalism to calculate cosmological correlators for pseudo-Hermitian systems. We study a model consists of massive symplectic fermions coupled to the primordial curvature perturbation. The three-point function for the primordial curvature perturbation is computed up to one-loop and compared to earlier work where the loop correction comes from a massive scalar boson. The two results differ by a minus sign. Therefore, the one loop correction to the three-point function cannot be used to distinguished scalar bosons and symplectic fermions. To conclude, we discuss possibilities where the scalar bosons and symplectic fermions may be distinguished.

hep-th↗
arXiv2024

On Wigner Degeneracy in Elko theory: Hermiticity and Dark Matter

In this paper, we provide a set of Hermitian interactions for quantum fields based on Elko, considering the recent achievements concerning the most general form of singular spinors and Wigner degeneracy. We consider Hermiticity and renormalizability a criterion to define the derivative Elko-Higgs interaction as the suitable candidate for a dark coupling. Then, the free parameters of the model are fixed by cosmological constraints on the dark matter abundance, bounds on the Higgs invisible decays, and limits on the electron-dark matter scattering mediated by the Higgs.

hep-ph↗
arXiv2024

Elko as an inflaton candidate

Elko is a spin-half fermion with a two-fold Wigner degeneracy and Klein-Gordon dynamics. In this paper, we show that in a spatially flat FLRW space-time, slow-roll inflation can be initiated by the homogeneous Elko fields. The inflaton is a composite scalar field obtained by contracting the spinor field with its dual. This is possible because the background evolution as described by the Friedmann equation is completely determined by the scalar field. This approach has the advantage that we do not need to specify the initial conditions for every component of the spinor fields. We derive the equation of motion for the inflaton and also show that this solution is an attractor. Finally, we examine the slow-roll parameters and the power-spectrum, showing that obtaining a behavior in agreement with observational requirements is hard to be obtained, unless one uses more complicated potentials, which may act a limitation of Elko inflation.

hep-th↗
arXiv2024

Equivalence of regular spinor fields

In the Lounesto classification, there are three types of regular spinors. They are classified by the condition that at least one of the scalar or pseudo scalar norms are non-vanishing. The Dirac spinors are regular spinors because their scalar and pseudo scalar norms are non-zero and zero respectively. We construct local and Lorentz-covariant fermionic fields from all three classes of regular spinors. By computing the invariants and bilinear covariants of the regular spinor fields, we show that they are physically equivalent to the Dirac fields in the sense that whatever interactions one writes down using the regular spinor fields, they can always be expressed in terms of the Dirac fields.

hep-th↗
arXiv2024

Mass dimension one fermions in FLRW space-time

Cosmelkology is the study of Elko in cosmology. Elko is a massive spin-half field of mass dimension one. Elko differs from the Dirac and Majorana fermions because it furnishes the irreducible representation of the extended Poincare group with a two-fold Wigner degeneracy where the particle and anti-particle states both have four degrees of freedom. Elko has a renormalizable quartic self interaction which makes it a candidate for self-interacting dark matter. We study Elko in the spatially flat FLRW space-time and find exact solutions in the de Sitter space. By choosing the appropriate solutions and phases, the fields satisfy the canonical anti-commutation relations and have the correct time evolutions in the flat space limit.

hep-th↗
arXiv2023

Irreducible representations of the inhomogeneous Lorentz group with two-fold Wigner degeneracy

Not all complete set of spinors can be used as expansion coefficients of a quantum field. In fact, Steven Weinberg established the uniqueness of Dirac spinors for this purpose provided: (a) one paid due attention to the multiplicative phases for each of the spinors, and (b) one paired these to creation and annihilation operators in a specific manner. This is implicit in his implementation of the rotational symmetry for the spin half quantum field. Among the numerous complete set of spinors that are available to a physicist, Elko occupies a unique status that allows it to enter as expansion coefficients of a quantum field without violating Weinberg's no go theorem. How this paradigm changing claim arises is the primary subject of this communication. Weinberg's no go theorem is evaded by exploiting a uniquely special feature of Elko that allows us to introduce a doubling of the particle-antiparticle degrees of freedom from four to eight. Weinberg had dismissed this degeneracy on the ground that, "no examples are known of particles that furnish unconventional representations of inversions." Here we will find that this degeneracy, once envisioned by Eugene Wigner, in fact gives rise to a quantum field that has all the theoretical properties required of dark matter.

hep-th↗
arXiv2023

Spin-half bosons with mass dimension three half: Evading the spin-statistics theorem

By exploiting the freedom in defining the dual of spinors, we report an unexpected theoretical discovery of a quantum field theory of spin-half bosons. It fulfils Dirac's 1969-70 observation that "there must be boson variables connected with electrons." The theory is local, Lorentz-invariant, and has a positive-definite Hamiltonian. We formulate the unitarity-preserving scattering theory to accommodate the new dual and the associated adjoint. A model of Yukawa interaction with spin-half bosons and fermions of equal masses is studied to explicitly show unitarity.

hep-th↗
arXiv2023

Generalized unitary evolution for symplectic scalar fermions

The theory of symplectic scalar fermion of LeClair and Neubert is studied. The theory evades the conventional spin-statistics theorem because its Hamiltonian is pseudo Hermitian. Here, we clarify the derivation of the symplectic currents and charges. By demanding the currents and charges to be pseudo Hermitian, the global symmetry of the free Lagrangian density reduces from Sp(2,C) to SU(2). By explicit calculations, we show that the LeClair-Neubert model of N quartic self-interacting scalar fermions admits generalized unitary evolution.

hep-th↗
arXiv2022

Mass dimension one fields with Wigner degeneracy: A theory of dark matter

Whatever dark matter is, it must be one irreducible unitary representation of the extended Lorentz group or another. We here develop a formalism of mass dimension one fermions and bosons of spin one half, and show that they provide natural dark matter candidates. By construction, they are covariant under space-time translations and boosts. However, incorporating the rotational symmetry is non-trivial and requires introducing a two-fold Wigner degeneracy thus doubling the degrees of freedom for particles and anti particles from two to four. With Wigner degeneracy, we have a well-defined theory of mass dimension one fields of spin one half that are physically distinct from the Dirac field. They are local, Lorentz covariant and have positive definite free Hamiltonians. The developed framework also has the potential to resolve the cosmological constant problem, and supply dark energy.

physics.gen-ph↗
arXiv2022

Mass dimension one fermions: Constructing darkness

Let $Θ$ be the Wigner time reversal operator for spin half and let $ϕ$ be a Weyl spinor. Then, for a left-transforming $ϕ$, the construct $ζ_λΘϕ^\ast$ yields a right-transforming spinor. If instead, $ϕ$ is a right-transforming spinor, then the construct $ζ_ρΘϕ^\ast$ results in a left-transforming spinor ($ζ_{λ,ρ}$ are phase factors). This allows us to introduce two sets of four-component spinors. Setting $ζ_λ$ and $ζ_ρ$ to $\pm i$ render all eight spinors as eigenspinor of the charge conjugation operator~$\mathcal{C}$ (called ELKO). This allows us to introduce two quantum fields. A calculation of the vacuum expectation value of the time-ordered product of the fields and their adjoints reveals the mass dimension of the fields to be one. Both fields are local in the canonical sense of quantum field theory. Interestingly, one of the fields is fermionic and the other bosonic. The mass dimension of the introduced fermionic fields and the matter fields of the Standard Model carry an intrinsic mismatch. As such, they provide natural darkness for the new fields with respect to the Standard Model doublets. The statistics and locality are controlled by a set of phases. These are explicitly given. Then we observe that in $p_μp^μ= m^2$, Dirac took the simplest square root of the $4\times 4$ identity matrix $I$ (in $I \times m^2 $, while introducing $γ_μp^μ$ as the square root of the left hand side of the dispersion relation), and as such he implicitly ignored the remaining fifteen. When we examine the remaining roots, we obtain additional bosonic and fermionic dark matter candidates of spin half. We point out that by early nineteen seventies, Dirac had suspected the existence of spin half bosons, in the same space as his fermions. Abstract truncated.

hep-ph↗
arXiv2021

Chiral phases for massive fermions and spinor classifications

We explore the physics of regular spinors in the Lounesto classification. These spinors are constructed by introducing two chiral phases. One is a degree of freedom present in choosing the $\gamma^{\mu}$ matrices that leaves the Lorentz generators invariant. Another is a degree of freedom allowed by the massive spin-half field that is unconstrained by Poincar\'{e} symmetry and locality. By choosing appropriate values of the two phases, we obtain all the classes of regular spinors. For the Dirac fermions, both phases are equal. We argue that the chiral phase of the Standard Model fermions is a new set of physical parameter. We find, the lepton chiral phases cannot be measured within the weak interaction. For quarks, their phases are conjectured to be identical. In general, to measure the phases between different fermionic generations would require interactions beyond the Standard Model.

hep-th↗
arXiv2021

Fermionic degeneracy and non-local contributions in flag-dipole spinors and mass dimension one fermions

We construct a mass dimension one fermionic field associated with flag-dipole spinors. These spinors are related to Elko (flag-pole spinors) by a one-parameter matrix transformation $\mathcal{Z}(z)$ where $z$ is a complex number. The theory is non-local and non-covariant. While it is possible to obtain a Lorentz-invariant theory via $τ$-deformation, we choose to study the effects of non-locality and non-covariance. Our motivation for doing so is explained. We show that a fermionic field with $|z|\neq1$ and $|z|=1$ are physically equivalent. But for fermionic fields with more than one value of $z$, their interactions are $z$-dependent thus introducing an additional fermionic degeneracy that is absent in the Lorentz-invariant theory. We study the fermionic self-interaction and the local $U(1)$ interaction. In the process, we obtained non-local contributions for fermionic self-interaction that have previously been neglected. For the local $U(1)$ theory, the interactions contain time derivatives that renders the interacting density non-commutative at space-like separation. We show that this problem can be resolved by working in the temporal gauge. This issue is also discussed in the context of gravity.

hep-th↗