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Multi-time Wave Functions

An Introduction

  • Unique and clearly written introduction to multi-time wave functions
  • Novel relativistic perspective on the nature of the quantum state
  • Includes exercises for self-study or teaching

Part of the book series: SpringerBriefs in Physics (SpringerBriefs in Physics)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-viii
  2. Introduction and Overview

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 1-15
  3. Consistency Conditions and Interaction Potentials

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 17-29
  4. Relativistic Point Interactions in 1\(+\)1 Dimensions

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 31-39
  5. Multi-time Quantum Field Theory

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 41-53
  6. Interior-Boundary Conditions for Multi-time Wave Functions

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 55-60
  7. Born’s Rule for Arbitrary Cauchy Surfaces

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 61-69
  8. Multi-time Integral Equations

    • Matthias Lienert, Sören Petrat, Roderich Tumulka
    Pages 71-80
  9. Back Matter

    Pages 81-89

About this book

The natural generalization of the quantum-mechanical N-particle wave function to relativistic space-time is a function of N space-time points, and thus of N time variables. This book, based on a collection of lectures given at a spring school in Tübingen in 2019, provides an accessible and concise introduction to the recent development of the theory of multi-time wave functions, their use in quantum field theory, their relation to detection probabilities, and the mathematical question of consistency of their time evolution equations. The book is intended for advanced students and researchers with an interest in relativity and quantum physics.

Authors and Affiliations

  • Fachbereich Mathematik, Eberhard-Karls-Universität Tübingen, Tübingen, Germany

    Matthias Lienert, Roderich Tumulka

  • Mathematical Sciences, Jacobs University Bremen, Bremen, Germany

    Sören Petrat

About the authors

Born in 1988 in Würzburg, Germany, Matthias Lienert studied physics in Göttingen and theoretical physics in Cambridge, UK. He obtained his PhD in Mathematics at Ludwig Maximilians University in Munich in 2015. Since then he has been a postdoctoral researcher in mathematical physics, in particular relativistic quantum theory, at Rutgers University, USA, and the University of Tübingen, Germany. 

Sören Petrat was born in 1985 in Castrop-Rauxel (Germany). After obtaining a PhD in mathematics from Ludwig Maximilians University Munich, he worked as a postdoctoral researcher at IST Austria, IAS Princeton, and Princeton University. Since 2017 he is Professor at Jacobs University Bremen. His field of research is mathematical physics, specifically many-body quantum mechanics and relativistic quantum physics.

Roderich Tumulka was born in 1972 in Frankfurt am Main (Germany), earned a Ph.D. in mathematics from Ludwig Maximilians University in Munich, taught at Rutgers University (USA) in 2007—2016, and has since taught at Eberhard Karls University in Tübingen (Germany). His field of research is mathematical physics, particularly the foundations of quantum mechanics, quantum field theory, and quantum statistical mechanics.

Bibliographic Information

Buy it now

Buying options

eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access