Methods Of Bosonic And Fermionic Path Integrals Representations: Continuum Random Geometry In Quantum Field Theory

M ETHODS OF B OSONIC AND F ERMIONIC PATH I NTEGRALS R EPRESENTATIONS : C ONTINUUM R ANDOM G EOMETRY IN Q UANTUM F IELD T HEORY No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services. M ETHODS OF B OSONIC AND F ERMIONIC PATH I NTEGRALS R EPRESENTATIONS : C ONTINUUM R ANDOM G EOMETRY IN Q UANTUM F IELD T HEORY L UIZ C.L. B OTELHO Nova Science Publishers, Inc. New York c 2009 by Nova Science Publishers, Inc.  All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter cover herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal, medical or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Library of Congress Cataloging-in-Publication Data Botelho, Luiz C. L. Methods of bosonic and fermionic path integrals representations : continuum random geometry in quantum field theory / Luiz C.L. Botelho. p. cm. Includes bibliographical references and index. ISBN 978-1-60741-908-2 (E-Book) 1. Path integrals. 2. Integral representations. I. Title. QC174.17.P27B679 2007 530.14’3–dc22 2007042443 Published by Nova Science Publishers, Inc.  New York For all those who have been struggling, resisting and finally prevailing in “Gulags” (even “Academic” ones.) To Nelma, Rafael and Gabriel – always at my side. Contents About This Monograph xi 1 Loop Space Path Integrals Representations for Euclidean Quantum Fields Path Integrals and the Covariant Path Integral 1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. The Bosonic Loop Space Formulation of the O(N)-Scalar Field Theory . . 1.3. A Fermionic Loop Space for QCD . . . . . . . . . . . . . . . . . . . . . . 1.4. Invariant Path Integration and the Covariant Functional Measure for Einstein Gr