On linear unitary transformations of two canonical variables

1989 ◽  
Vol 30 (5) ◽  
pp. 993-999 ◽  
Author(s):  
Jerzy F. Plebański ◽  
J. D. Finley
Keyword(s):  
Canonical Variables ◽  
Unitary Transformations

scholarly journals MINISUPERSPACES: OBSERVABLES AND QUANTIZATION

1993 ◽  
Vol 02 (01) ◽  
pp. 15-50 ◽  
Author(s):  
ABHAY ASHTEKAR ◽  
RANJEET TATE ◽  
CLAES UGGLA
Keyword(s):  
Quantum Theory ◽  
Phase Space ◽  
Canonical Transformation ◽  
Parameter Family ◽  
Hamiltonian Constraint ◽  
Canonical Coordinates ◽  
Quantum Theories ◽  
Canonical Variables ◽  
Unitary Transformations ◽  
Homogeneous Cosmologies

A canonical transformation is performed on the phase space of a number of homogeneous cosmologies to simplify the form of the scalar (or Hamiltonian) constraint. Using the new canonical coordinates, it is then easy to obtain explicit expressions of Dirac observables, i.e. phase-space functions which commute weakly with the constraint. This, in turn, enables us to carry out a general quantization program to completion. We are also able to address the issue of time through “deparametrization” and discuss physical questions such as the fate of initial singularities in the quantum theory. We find that they persist in the quantum theory in spite of the fact that the evolution is implemented by a one-parameter family of unitary transformations. Finally, certain of these models admit conditional symmetries which are explicit already prior to the canonical transformation. These can be used to pass to the quantum theory following an independent avenue. The two quantum theories — based, respectively, on Dirac observables in the new canonical variables and conditional symmetries in the original ADM variables — are compared and shown to be equivalent.

THYMUS VARIABILITY IN WHITE RATS EXPOSED TO FORMALDEHYDE

2019 ◽  
pp. 105-116
Author(s):  
V.N. Voloshin ◽  
I.S. Voloshina ◽  
I.Yu. Vash
Keyword(s):  
White Male ◽  
Principal Component ◽  
Middle Part ◽  
Procrustes Analysis ◽  
Male Rats ◽  
Canonical Variables ◽  
Generalized Procrustes Analysis ◽  
White Rats ◽  
Main Component ◽  
Formaldehyde Inhalation

The aim of the paper is to study thymus variability in white rats, which were exposed to formaldehyde, and to compare these data with the indicators in control animals. Materials and Methods. The trial enrolled 72 white male rats, initial body weight 40–50 g. The animals were divided into 2 groups (36 rats in each). The first group consisted of control rats. Animals of the second group were exposed to formaldehyde inhalation, 2.766 mg/m3. To characterize the variability of the organ size, centroids were determined. The superposition of landmark configurations was performed using the generalized Procrustes analysis method, MorphoJ 1.06d program. The principal component analysis and canonical analysis of the obtained data were carried out. Results. One-Way ANOVA revealed a high level of intergroup differences in Procrust distance (F=1.34; p<0.0001). The significant effect of the duration of formaldehyde exposure on centroid size was established. The Kruskal-Wallis criterion was 19.778 (p=0.0014). The analysis of the principal components indicated that each of the first 10 components stands for more than 1 % of Procrustes coordinate variance. In this case, the first 7 components compatibly explain 91.398 % of thymus variability. The proportion of the first main component to the total variance of the Procrustes coordinates is 40.236 %. PC1 (-) shows changes in the thymus shape, mostly affecting the tops of its lobes, the middle part of the right boundary and the entire left thymus boundary. The scattering ellipses of the thymus ordinates in rats exposed to formaldehyde, in the first two canonical variables are located higher than those in the control animals. Conclusion. Formaldehyde inhalation leads to thymus changes in white rat. The most significant differences with control data are determined along the second canonical variable. Keywords: thymus, form, rat, formaldehyde, geometric morphometry. Цель. Изучение изменчивости формы тимуса белых крыс, находившихся в условиях влияния формальдегида, и сравнение этих данных с показателями, полученными у контрольных животных. Материалы и методы. Работа выполнена на 72 белых крысах-самцах с начальной массой тела 40–50 г. Животные были разделены на 2 серии (по 36 крыс). Первую серию составляли контрольные крысы. Животные второй серии подвергались ингаляционному воздействию формальдегида (ФА) в концентрации 2,766 мг/м3. Для характеристики изменчивости размеров органов определяли размер их центроидов. Процедуру суперимпозиции конфигураций ландмарок выполняли методом генерализованного прокрустова анализа с использованием программы MorphoJ 1.06d. Проводили анализ главных компонент и канонический анализ полученных данных. Результаты. Однофакторный дисперсионный анализ выявил высокий уровень межгрупповых различий по показателю прокрустовых расстояний (F=1,34; р<0,0001). Установлено значительное влияние продолжительности нахождения животных в условиях воздействия ФА на размер центроида. Критерий Краскела–Уоллиса составил 19,778 (р=0,0014). Анализ главных компонент указывал на то, что каждая из первых 10 компонент объясняет более 1 % дисперсии прокрустовых координат. При этом первые 7 компонент совместно объясняют 91,398 % изменчивости формы тимуса. Вклад первой главной компоненты в общую дисперсию прокрустовых координат составляет 40,236 %. РС1 (–) показывает изменения формы тимуса, в большей степени затрагивающие верхушки его долей, среднюю часть правого контура и весь левый контур тимуса. Эллипсы рассеивания ординат тимусов, принадлежащих крысам, подвергавшимся влиянию ФА, в пространстве первых двух канонических переменных расположены выше по отношению к таковым контрольных животных. Заключение. Ингаляционное воздействие формальдегида приводит к изменению формы тимуса белых крыс. Наибольшие различия с контрольными данными определяются вдоль второй канонической переменной. Ключевые слова: тимус, форма, крыса, формальдегид, геометрическая морфометрия.

Hamiltonian Mechanics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Angular Momentum ◽  
Jacobi Equation ◽  
Modern Theory ◽  
Hamiltonian Mechanics ◽  
Lagrangian Mechanics ◽  
Canonical Transformations ◽  
Canonical Variables ◽  
Light Waves ◽  
Hamilton Jacobi Equation ◽  
Common Action

Hamilton’s genius was to understand what were the true variables of mechanics (the “p − q,” conjugate coordinates, or canonical variables), and this led to Hamilton’s Mechanics which could obtain qualitative answers to a wider ranger of problems than Lagrangian Mechanics. It is explained how Hamilton’s canonical equations arise, why the Hamiltonian is the “central conception of all modern theory” (quote of Schrödinger’s), what the “p − q” variables are, and what phase space is. It is also explained how the famous conservation theorems arise (for energy, linear momentum, and angular momentum), and the connection with symmetry. The Hamilton-Jacobi Equation is derived using infinitesimal canonical transformations (ICTs), and predicts wavefronts of “common action” spreading out in (configuration) space. An analogy can be made with geometrical optics and Huygen’s Principle for the spreading out of light waves. It is shown how Hamilton’s Mechanics can lead into quantum mechanics.

scholarly journals Experimental demonstrations of unconditional security in a purely classical regime

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Byoung S. Ham
Keyword(s):  
Quantum Key Distribution ◽  
Key Distribution ◽  
Unconditional Security ◽  
Zehnder Interferometer ◽  
Experimental Demonstration ◽  
Orthogonal Bases ◽  
Unitary Transformations ◽  
Mach Zehnder Interferometer

AbstractSo far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach–Zehnder interferometer. Here, the first experimental demonstration of the USCKD protocol is presented.

Lie groups and unitary transformations in ligand field theory

1983 ◽  
Vol 23 (1) ◽  
pp. 169-183 ◽  
Author(s):  
Chia-Chung Sun ◽  
Yan-De Han ◽  
Be-Fu Li ◽  
Qian-Shu Li
Keyword(s):  
Field Theory ◽  
Lie Groups ◽  
Ligand Field ◽  
Ligand Field Theory ◽  
Unitary Transformations

CONSISTENT CANONICAL QUANTIZATION OF THE CHIRAL SCHWINGER MODEL

1991 ◽  
Vol 06 (21) ◽  
pp. 3823-3841 ◽  
Author(s):  
FUAD M. SARADZHEV
Keyword(s):  
Canonical Quantization ◽  
Bound State ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Schwinger Model ◽  
Canonical Variables ◽  
Bound State Spectrum

For the chiral Schwinger model, the canonical quantization formulation consistent with the Gauss law constraint is developed. This requires modification of the canonical variables of the model. The formulation presented is unitary and gauge-invariant under modified gauge transformations. The bound state spectrum of the model is established.

scholarly journals Graphical description of unitary transformations on hypergraph states

2017 ◽  
Vol 50 (19) ◽  
pp. 19LT01 ◽  
Author(s):  
Mariami Gachechiladze ◽  
Nikoloz Tsimakuridze ◽  
Otfried Gühne
Keyword(s):  
Unitary Transformations
Sign in / Sign up

Export Citation Format

Share Document