scholarly journals ON UNITARY TIME EVOLUTION IN GOWDY T3 COSMOLOGIES

2002 ◽  
Vol 11 (09) ◽  
pp. 1451-1468 ◽  
Author(s):  
ALEJANDRO CORICHI ◽  
JERÓNIMO CORTEZ ◽  
HERNANDO QUEVEDO
Keyword(s):  
Scalar Field ◽  
Degrees Of Freedom ◽  
Canonical Quantization ◽  
Quantum States ◽  
Classical Dynamics ◽  
Two Dimensional ◽  
Symplectic Transformation ◽  
Internal Time ◽  
Curved Manifolds ◽  
Free Scalar

A non-perturbative canonical quantization of the Gowdy T3 polarized models is considered here. This approach profits from the equivalence between the symmetry reduced model and 2 + 1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is made, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a two-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both the quantization of fields on curved manifolds and other physically relevant questions regarding the initial singularity are discussed.

scholarly journals Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
José Velhinho
Keyword(s):  
Scalar Field ◽  
Canonical Quantization ◽  
Field Theories ◽  
Quantum Fields ◽  
Theoretical Methods ◽  
Local Properties ◽  
Free Scalar ◽  
Free Fields ◽  
Field Behaviour

This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present two characterizations of the support of these measures. The first characterization concerns local properties of the quantum fields, whereas for the second one we introduce a sequence of variables that test the field behaviour at large distances, thus allowing distinguishing between the typical quantum fields associated with different values of the mass.

scholarly journals Free Scalar Fields in Finite Volume Are Holographic

Universe ◽  
2019 ◽  
Vol 5 (12) ◽  
pp. 223
Author(s):  
Csaba Balázs
Keyword(s):  
Scalar Field ◽  
Surface Area ◽  
Finite Volume ◽  
Degrees Of Freedom ◽  
Scalar Fields ◽  
Flat Space ◽  
Linear Size ◽  
Energy Mode ◽  
Free Scalar ◽  
Quantized Field

This brief note presents a back-of-the-envelope calculation showing that the number of degrees of freedom of a free scalar field in expanding flat space equals the surface area of the Hubble volume in Planck units. The logic of the calculation is the following. The amount of energy in the Hubble volume scales with its linear size, consequently the volume can only contain a finite number of quantized field modes. Since the momentum of the lowest energy mode scales inversely with the linear size of the volume, the maximal number of such modes in the volume scales with its surface area. It is possible to show that when the number of field modes is saturated the modes are confined to the surface of the volume. Gravity only enters this calculation as a regulator, providing a finite volume that contains the field, the entire calculation is done in flat space. While this toy model is bound to be incomplete, it is potentially interesting because it reproduces the defining aspects of holography, and advocates a regularization of the quantum degrees of freedom based on Friedmann’s equation.

scholarly journals THE CASIMIR ENERGY FOR TWO-DIMENSIONAL DEFORMED SPHERE

1995 ◽  
Vol 10 (09) ◽  
pp. 755-760
Author(s):  
N. SHTYKOV ◽  
D. V. VASSILEVICH
Keyword(s):  
Scalar Field ◽  
Casimir Energy ◽  
Two Dimensional ◽  
Free Scalar

We compute the Casimir energy for a free scalar field on the spaces [Formula: see text] where [Formula: see text] is two-dimensional deformed two-sphere.

scholarly journals TIME AND TACHYON

2003 ◽  
Vol 18 (26) ◽  
pp. 4869-4888 ◽  
Author(s):  
ASHOKE SEN
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Quantum Gravity ◽  
Quantum Cosmology ◽  
Canonical Quantization ◽  
Recent Analysis ◽  
Late Time ◽  
Classical Dynamics ◽  
One To One ◽  
Definition Of

Recent analysis suggests that the classical dynamics of a tachyon on an unstable D-brane is described by a scalar Born–Infeld type action with a runaway potential. The classical configurations in this theory at late time are in one to one correspondence with the configuration of a system of noninteracting (incoherent), nonrotating dust. We discuss some aspects of canonical quantization of this field theory coupled to gravity, and explore, following an earlier work on this subject, the possibility of using the scalar field (tachyon) as the definition of time in quantum cosmology. At late "time" we can identify a subsector in which the scalar field decouples from gravity and we recover the usual Wheeler–de Witt equation of quantum gravity.

scholarly journals CANONICAL QUANTIZATION OF TWO-DIMENSIONAL GAUGE FIELDS

1994 ◽  
Vol 09 (18) ◽  
pp. 3153-3178 ◽  
Author(s):  
JAMES E. HETRICK
Keyword(s):  
Gauge Theory ◽  
Ground State ◽  
Degrees Of Freedom ◽  
Lattice Gauge Theory ◽  
Canonical Quantization ◽  
Casimir Energy ◽  
Gauge Fields ◽  
Two Dimensional ◽  
Lattice Gauge ◽  
Canonical Coordinate

SU (N) gauge fields on a cylindrical space-time are canonically quantized via two routes revealing almost equivalent but different quantizations. After removal of all continuous gauge degrees of freedom, the canonical coordinate Aµ (in the Cartan subalgebra [Formula: see text]) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop W, projecting out gauge-invariant wave functions on the group manifold G. After a Casimir energy related to the curvature of SU (N) is added to the compact spectrum, it is seen to be a subset of the noncompact spectrum. States of the two quantizations with corresponding energy are shifted relative to each other, such that the ground state on G, χ0(W), is the first excited state Ψ1(Aµ) on [Formula: see text]. The ground state Ψ0(Aµ) does not appear in the character spectrum, as its lift is not globally defined on G. Implications for lattice gauge theory and the sum-over-maps representation of two-dimensional QCD are discussed.

Quantum simulations

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Ab Initio ◽  
Quantum Monte Carlo ◽  
Degrees Of Freedom ◽  
Small Region ◽  
Time Correlation ◽  
Ab Initio Molecular Dynamics ◽  
Classical Dynamics ◽  
Integral Methods ◽  
Quantum Time ◽  
Low Mass

This chapter covers the introduction of quantum mechanics into computer simulation methods. The chapter begins by explaining how electronic degrees of freedom may be handled in an ab initio fashion and how the resulting forces are included in the classical dynamics of the nuclei. The technique for combining the ab initio molecular dynamics of a small region, with classical dynamics or molecular mechanics applied to the surrounding environment, is explained. There is a section on handling quantum degrees of freedom, such as low-mass nuclei, by discretized path integral methods, complete with practical code examples. The problem of calculating quantum time correlation functions is addressed. Ground-state quantum Monte Carlo methods are explained, and the chapter concludes with a forward look to the future development of such techniques particularly to systems that include excited electronic states.

scholarly journals Weak cosmic censorship with self-interacting scalar and bound on charge to mass ratio

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Yan Song ◽  
Tong-Tong Hu ◽  
Yong-Qiang Wang
Keyword(s):  
Scalar Field ◽  
Scalar Fields ◽  
Cosmic Censorship ◽  
Mass Ratio ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Free Scalar ◽  
The One ◽  
Nonzero Scalar ◽  
Large Charge

Abstract We study the model of four-dimensional Einstein-Maxwell-Λ theory minimally coupled to a massive charged self-interacting scalar field, parameterized by the quartic and hexic couplings, labelled by λ and β, respectively. In the absence of scalar field, there is a class of counterexamples to cosmic censorship. Moreover, we investigate the full nonlinear solution with nonzero scalar field included, and argue that these counterexamples can be removed by assuming charged self-interacting scalar field with sufficiently large charge not lower than a certain bound. In particular, this bound on charge required to preserve cosmic censorship is no longer precisely the weak gravity bound for the free scalar theory. For the quartic coupling, for λ < 0 the bound is below the one for the free scalar fields, whereas for λ > 0 it is above. Meanwhile, for the hexic coupling the bound is always above the one for the free scalar fields, irrespective of the sign of β.

scholarly journals Gaussian quantum states can be disentangled using symplectic rotations

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Maurice A. de Gosson
Keyword(s):  
Quantum State ◽  
Covariance Matrices ◽  
Quantum States ◽  
Weyl Quantization ◽  
Symplectic Transformation ◽  
Metaplectic Operator

AbstractWe show that every Gaussian mixed quantum state can be disentangled by conjugation with a passive symplectic transformation, that is a metaplectic operator associated with a symplectic rotation. The main tools we use are the Werner–Wolf condition on covariance matrices and the symplectic covariance of Weyl quantization. Our result therefore complements a recent study by Lami, Serafini, and Adesso.

scholarly journals Thermos Array: Two-Dimensional Sparse Array with Reduced Mutual Coupling

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Lei Sun ◽  
Minglei Yang ◽  
Baixiao Chen
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Mutual Coupling ◽  
Doa Estimation ◽  
Two Dimensional ◽  
Spatial Smoothing ◽  
Planar Arrays ◽  
Half Wavelength ◽  
Planar Array ◽  
Small Spacing

Sparse planar arrays, such as the billboard array, the open box array, and the two-dimensional nested array, have drawn lots of interest owing to their ability of two-dimensional angle estimation. Unfortunately, these arrays often suffer from mutual-coupling problems due to the large number of sensor pairs with small spacing d (usually equal to a half wavelength), which will degrade the performance of direction of arrival (DOA) estimation. Recently, the two-dimensional half-open box array and the hourglass array are proposed to reduce the mutual coupling. But both of them still have many sensor pairs with small spacing d, which implies that the reduction of mutual coupling is still limited. In this paper, we propose a new sparse planar array which has fewer number of sensor pairs with small spacing d. It is named as the thermos array because its shape seems like a thermos. Although the resulting difference coarray (DCA) of the thermos array is not hole-free, a large filled rectangular part in the DCA can be facilitated to perform spatial-smoothing-based DOA estimation. Moreover, it enjoys closed-form expressions for the sensor locations and the number of available degrees of freedom. Simulations show that the thermos array can achieve better DOA estimation performance than the hourglass array in the presence of mutual coupling, which indicates that our thermos array is more robust to the mutual-coupling array.

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