Operator formalism of quantum mechanics

نویسنده

  • Jan Naudts
چکیده

This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The mathematical foundation of this approach comes from a recent paper of Naudts and Kuna on covariance systems. The standard representation of quantum mechanics is derived. Next, spin and mass of a quantum particle are explained as labels of projective representations of the Galilei group.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Positive - Operator - Valued Time Observable in Quantum Mechanics

We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.

متن کامل

Product Operator Formalism: A Brief Introduction

Multiple spin systems allow for the presence of quantum coherence and spin-spin coupling interactions. Traditionally, density operator formalism is used to describe these systems; however, the use of this formalism often clouds intuition making it a cumbersome tool. Here we introduce a third formalism constructed from the density operator formalism with a direct connection to a non-classical in...

متن کامل

Quantum Causal Histories and the Directed Graph Operator Framework

A mathematical formalism called Quantum Causal Histories was recently invented as an attempt to describe causality within a quantum theory of gravity. Fundamental examples include quantum computers. We show there is a connection between this formalism and the directed graph operator framework from the theory of operator algebras.

متن کامل

No Labeling Quantum Mechanics of Indiscernible Particles

Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobserv...

متن کامل

Algebra of Effects in the Formalism of Quantum Mechanics on Phase Space as an M. V. and a Heyting Effect Algebra∗

An effect in quantum mechanics on a Hilbert space H is an operator A in H such that 0 ≤ A ≤ I , and two effects, A and B, are added to get A⊕ B iff 0 ≤ A⊕ B ≤ I, where A⊕ B is the operator addition. We wish to specialize this concept to the effects that arise naturally in the formalism of quantum mechanics on phase space (Schroeck, 1996). From this, we will have an immediate generalization to H...

متن کامل

The Wigner-weyl Formalism and the Relativistic Semi-classical Approximation 1

The relativistic semi-classical approximation for a free massive particle is studied using the Wigner-Weyl formalism. A non-covariant Wigner function is defined using the Newton-Wigner position operator. The perturbative solution for the time evolution is found. Causality is found to be perturbatively respected. 1 1 Introduction. The Wigner-Weyl formalism [1] offers a classical-like formulation...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000