Related papers: Linear Canonical Transformations in Relativistic Q…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
Lithium is a typical quantum solid, characterized by cubic structures at ambient pressure. As the pressure increases, it forms more complex structures and undergoes a metal-to-semiconductor transformation, complicating theoretical and…
Since their first introduction, Quantum Reference Frame (QRF) transformations have been extensively discussed, generalising the covariance of physical laws to the quantum domain. Despite important progress, a formulation of QRF…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
Due to the rapid development of quantum computing, the compact representation of quantum operations based on decision diagrams has been received more and more attraction. Since variable orders have a significant impact on the size of the…
The CPT theorem states that a unitary and Lorentz-invariant theory must also be invariant under a discrete symmetry $\mathbf{CRT}$ which reverses charge, time, and one spatial direction. In this article, we study a $\mathbb{Z}_2 \times…
In this paper, we introduce the notion of windowed linear canonical transform in biquaternion setting namely Biquaternion Windowed Linear Canonical Transform (BiQWLCT) and various properties of BiQWLCT, such as linearity, shift, parity,…
A free quantum field theory with Lorentz symmetry is derived for spin-half symplectic fermions in 2+1 dimensions. In particular, we show that fermionic spin-half fields may be canonically quantized in a free theory with a Klein-Gordon…
Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
Arbitrarily small changes in the commutation relations suffice to transform the usual singular quantum theories into regular quantum theories. This process is an extension of canonical quantization that we call general quantization. Here we…
A novel canonical transformation is offered as the mean for studying properties of a system of strongly correlated electrons. As an example of the utility of the transformation, it is used to demonstrate the existence of a quantum phase…
In this article, we give a new definition of the linear canonical Stockwell transform (LCST) and study its basic properties along with the inner product relation, reconstruction formula and also characterize the range of the transform and…
First, some superluminal phenomena and experiments are introduced briefly. Next, based on the basic principles of the special relativity, the Lorentz transformation (LT) with smaller velocity and the general Lorentz transformation (GLT)…
We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations.…
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under…
Light-front quantum chromodynamics may lead to an accurate constituent approximation for the low-energy properties of hadrons. This requires a cutoff that violates explicit gauge invariance and Lorentz covariance, leading to the calculation…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in…
In this paper the theory of time-dependent and time-independent canonical transformations is considered from a geometric perspective. Both the geometric formalism and the coordinate based approach are described in detail. In particular,…