اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDirac and the Path Integral
114
0
0.0
(
0
)
تأليف
N. D. Hari Dass
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Through a very careful analysis of Diracs 1932 paper on the Lagrangian in Quantum Mechanics as well as the second and third editions of his classic book {it The Principles of Quantum Mechanics}, I show that Diracs contributions to the birth of the path-integral approach to quantum mechanics is not restricted to just his seminal demonstration of how Lagrangians appear naturally in quantum mechanics, but that Dirac should be credited for creating a path-integral which I call {it Dirac path-integral} which is far more general than Feynmans while possessing all its desirable features. On top of it, the Dirac path-integral is fully compatible with the inevitable quantisation ambiguities, while the Feynman path-integral can never have that full consistency. In particular, I show that the claim by Feynman that for infinitesimal time intervals, what Dirac thought were analogues were actually proportional can not be correct always. I have also shown the conection between Dirac path-integrals and the Schrodinger equation. In particular, it is shown that each choice of Dirac path-integral yields a {it quantum Hamiltonian} that is generically different from what the Feynman path-integral gives, and that all of them have the same {it classical analogue}. Diracs method of demonstrating the least action principle for classical mechanics generalizes in a most straightforward way to all the generalized path-integrals.
قيم البحث
اقرأ أيضاً
The resolvent of supersymmetric Dirac Hamiltonian is studied in detail. Due to supersymmetry the squared Dirac Hamiltonian becomes block-diagonal whose elements are in essence non-relativistic Schrodinger-type Hamiltonians. This enables us to find a
Feynman-type path-integral representation of the resulting Greens functions. In addition, we are also able to express the spectral properties of the supersymmetric Dirac Hamiltonian in terms of those of the non-relativistic Schrodinger Hamiltonians. The methods are explicitly applied to the free Dirac Hamiltonian, the so-called Dirac oscillator and a generalization of it. The general approach is applicable to systems with good and broken supersymmetry.
Work statistics characterizes important features of a non-equilibrium thermodynamic process. But the calculation of the work statistics in an arbitrary non-equilibrium process is usually a cumbersome task. In this work, we study the work statistics i
n quantum systems by employing Feynmans path-integral approach. We derive the analytical work distributions of two prototype quantum systems. The results are proved to be equivalent to the results obtained based on Schr{o}dingers formalism. We also calculate the work distributions in their classical counterparts by employing the path-integral approach. Our study demonstrates the effectiveness of the path-integral approach to the calculation of work statistics in both quantum and classical thermodynamics, and brings important insights to the understanding of the trajectory work in quantum systems.
We derive some non-perturbative results in 1+1 and 2+1 dimensions within the context of the particle path-integral representation for a Dirac field propagator in the presence of an external field, in a formulation introduced by Migdal in 1986. We con
sider the specific properties of the path-integral expressions corresponding to the 1+1 and 2+1 dimensional cases, presenting a derivation of the chiral anomaly in the former and of the Chern-Simons current in the latter. We also discuss particle propagation in constant electromagnetic field backgrounds.
Quantum Monte Carlo belongs to the most accurate simulation techniques for quantum many-particle systems. However, for fermions, these simulations are hampered by the sign problem that prohibits simulations in the regime of strong degeneracy. The sit
uation changed with the development of configuration path integral Monte Carlo (CPIMC) by Schoof textit{et al.} [T. Schoof textit{et al.}, Contrib. Plasma Phys. textbf{51}, 687 (2011)] that allowed for the first textit{ab initio} simulations for dense quantum plasmas. CPIMC also has a sign problem that occurs when the density is lowered, i.e. in a parameter range that is complementary to traditional QMC formulated in coordinate space. Thus, CPIMC simulations for the warm dense electron gas are limited to small values of the Brueckner parameter -- the ratio of the interparticle distance to the Bohr radius -- $r_s=bar{r}/a_B lesssim 1$. In order to reach the regime of stronger coupling (lower density) with CPIMC, here we investigate additional restrictions on the Monte Carlo procedure. In particular, we introduce two differe
It is commonly assumed that zero and non-zero photon mass would lead to qualitatively different physics. For example, massless photon has two polarization degrees of freedom, while massive photon at least three. This feature seems counter-intuitive.
In this paper we will show that if we change propagator by setting $i epsilon$ (needed to avoid poles) to a finite value, and also introduce it in a way that breaks Lawrentz symmetry, then we would obtain the continuous transition we desire once the speed of the photons is large enough with respect to preferred frame. The two transverse polarization degrees of freedom will be long lived, while longitudinal will be short lived. Their lifetime will be near-zero if $m ll sqrt{epsilon}$, which is where the properties of two circular polarizations arize. The $i epsilon$ corresponds to the intensity of Menskys continuous measurement and the short lifetime of the longitudinal photons can be understood as the conversion of quantum degrees of freedom (photons) into classical ones by the measurement device (thus getting rid of the former). While the classical trajectory of the longitudinal photons does arize, it plays no physical role due to quantum Zeno effect: intuitively, it is similar to an electron being kept at a ground state due to continuous measurement.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
