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title: "The Quantum Theory of Fields: Volume 1, Foundations"
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# The Quantum Theory of Fields: Volume 1, Foundations

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## Description

In The Quantum Theory of Fields, Nobel Laureate Steven Weinberg combines his exceptional physical insight with his gift for clear exposition to provide a self-contained, comprehensive, and up-to-date introduction to quantum field theory. This is a two-volume work. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before, and emphasizing the reasons why such a theory should describe nature. After a brief historical outline, the book begins anew with the principles about which we are most certain, relativity and quantum mechanics, and the properties of particles that follow from these principles. Quantum field theory emerges from this as a natural consequence. The author presents the classic calculations of quantum electrodynamics in a thoroughly modern way, showing the use of path integrals and dimensional regularization. His account of renormalization theory reflects the changes in our view of quantum field theory since the advent of effective field theories. The book's scope extends beyond quantum electrodynamics to elementary particle physics, and nuclear physics. It contains much original material, and is peppered with examples and insights drawn from the author's experience as a leader of elementary particle research. Problems are included at the end of each chapter. This work will be an invaluable reference for all physicists and mathematicians who use quantum field theory, and it is also appropriate as a textbook for graduate students in this area.

Review: A compelling tour de force--with an inspiring treatment of the Spin Statistics Theorem - I perused my library's copy of this book when I first began to study QTF. At that early point, I found Weinberg's detailed exposition to be overwhelming. Now, after reading half of Ryder's Quantum Field Theory , a quarter of Peskin and Schroeder's An Introduction To Quantum Field Theory (Frontiers in Physics) , and half of Zee's Quantum Field Theory in a Nutshell: Second Edition (In a Nutshell (Princeton)) , I have bought my own copy of Weinberg and I have dived in head first. After taking a few weeks to orient myself, I now find myself entranced by Weinberg's discussion. I have genuine difficulty putting this book down! Weinberg provides an informative first chapter on the history of QTF. The second chapter on relativistic quantum theory goes well with Ryder's discussion of this topic. Chapter three is on S-matrix scattering theory. I also enjoyed Weinberg's use of the Cluster Decomposition Principle in Chapter 4 as a lead in and physical motivation for his lucid discussion of Feynman diagrams in Chapter 6. Chapter 5 deserves special mention for its a comprehensive discussion of the Spin Statistics Theorem which deals with both Fermions and Bosons in one fell swoop. The reader needs some help, however, in order to follow Weinberg's comprehensive treatment of this topic. Some useful insight can be gleaned from the pdf file of the lecture posted online by Bolvan of the University of Texas on the Spin Statistics Theorem. Essentially Weinberg is seen to express the commutators or anticommutators of fields phi(x) and phi(y) in terms of spin sums. Much insight into spin sums for spins larger than 1/2 can be extracted from Weinberg's paper Phys. Rev. 133, B1318 (1964) that is part of reference 1 cited in Chapter 5. In an Appendix of Weinberg's 1964 paper one learns that identities for hyperbolic functions are useful in determining the spin sums for different values of spin (e.g 1/2,1,3/2,etc.). Using these identities, the expression exp(-2tp.J)=cosh(2tp.J)-sinh(2tp.J) {where p is a unit vector parallel to the three momentum and J is angular momentum} can be expressed in terms of 3-momentum P and energy E (with P/m=sinh(t); E/m=cosh(t), where m is the particle mass). Before reading Weinberg's treatment, I was only familiar with spin sums for spin 1/2 Fermions (see for example Peskin and Schroeder pp.48-49). In spite of reading Weinberg's papers on the Spin Statistics Theorem, however, I felt that I was still missing a great deal of the insight needed to properly understand this important concept. Although Weinberg provides a sufficiently detailed discussion of the symmetries inherent in a massive particle, including the little group that corresponds to those symmetries, his treatment of massless particles left me confused. Luckily I found a more detailed discussion of the symmetries of massless particles in the work of Y.S. Kim and coworkers. In addition to many journal articles on the subject, including many co-authored with Wigner himself, Kim and his colleague M.E. Noz have written two books which treat this topic: Theory and Applications of the Poincaré Group (Fundamental Theories of Physics) ; Phase Space Picture of Quantum Mechanics: Group Theoretical Approach (World Scientific Lecture Notes in Physics) . I have read the latter of these two books and have found it be extremely helpful! I should also note that there is a potential difficulty and source of confusion (as one other reviewer has already mentioned) due to Weinberg's choice of metric. Instead of g00=1; g11=g22=g33=-1, Weinberg goes with g00=-1; g11=g22=g33=1. Also, rather than describing a point in space-time as (t,x,y,z) like in most other QFT books, Weinberg orders the space-time coordinates as (x,y,z,t). Weinberg's conventions change the appearance of many of the equations, space-time matrices, and four vectors. As a result the Lorentz transformation matrices now look quite different. The dot product of the four vectors p and x changes sign using Weinberg's conventions, so that what would be exp(-p.r) in Ryder or Peskin and Schroeder becomes exp(+p.r) in Weinberg. Although I will eventually get used to Weinberg's conventions, I felt that I should post these observations as an alert to others who might consider dedicating themselves to the study of Weinberg.
Review: QFT classic - More than any other book on quantum field theory, Weinberg’s textbook has helped me feel that I almost understand what is really going on. The notation and conventions can be a little hard to work with.

## Features

- Used Book in Good Condition

## Technical Specifications

| Specification | Value |
|---------------|-------|
| Best Sellers Rank | #1,135,866 in Books ( See Top 100 in Books ) #141 in Waves & Wave Mechanics (Books) #518 in Mathematical Physics (Books) #889 in Quantum Theory (Books) |
| Customer Reviews | 4.4 out of 5 stars 115 Reviews |

## Images

![The Quantum Theory of Fields: Volume 1, Foundations - Image 1](https://m.media-amazon.com/images/I/61g0LFOwINL.jpg)

## Customer Reviews

### ⭐⭐⭐⭐⭐ A compelling tour de force--with an inspiring treatment of the Spin Statistics Theorem
*by U***S on January 2, 2011*

I perused my library's copy of this book when I first began to study QTF. At that early point, I found Weinberg's detailed exposition to be overwhelming. Now, after reading half of Ryder's Quantum Field Theory , a quarter of Peskin and Schroeder's An Introduction To Quantum Field Theory (Frontiers in Physics) , and half of Zee's Quantum Field Theory in a Nutshell: Second Edition (In a Nutshell (Princeton)) , I have bought my own copy of Weinberg and I have dived in head first. After taking a few weeks to orient myself, I now find myself entranced by Weinberg's discussion. I have genuine difficulty putting this book down! Weinberg provides an informative first chapter on the history of QTF. The second chapter on relativistic quantum theory goes well with Ryder's discussion of this topic. Chapter three is on S-matrix scattering theory. I also enjoyed Weinberg's use of the Cluster Decomposition Principle in Chapter 4 as a lead in and physical motivation for his lucid discussion of Feynman diagrams in Chapter 6. Chapter 5 deserves special mention for its a comprehensive discussion of the Spin Statistics Theorem which deals with both Fermions and Bosons in one fell swoop. The reader needs some help, however, in order to follow Weinberg's comprehensive treatment of this topic. Some useful insight can be gleaned from the pdf file of the lecture posted online by Bolvan of the University of Texas on the Spin Statistics Theorem. Essentially Weinberg is seen to express the commutators or anticommutators of fields phi(x) and phi(y) in terms of spin sums. Much insight into spin sums for spins larger than 1/2 can be extracted from Weinberg's paper Phys. Rev. 133, B1318 (1964) that is part of reference 1 cited in Chapter 5. In an Appendix of Weinberg's 1964 paper one learns that identities for hyperbolic functions are useful in determining the spin sums for different values of spin (e.g 1/2,1,3/2,etc.). Using these identities, the expression exp(-2tp.J)=cosh(2tp.J)-sinh(2tp.J) {where p is a unit vector parallel to the three momentum and J is angular momentum} can be expressed in terms of 3-momentum P and energy E (with P/m=sinh(t); E/m=cosh(t), where m is the particle mass). Before reading Weinberg's treatment, I was only familiar with spin sums for spin 1/2 Fermions (see for example Peskin and Schroeder pp.48-49). In spite of reading Weinberg's papers on the Spin Statistics Theorem, however, I felt that I was still missing a great deal of the insight needed to properly understand this important concept. Although Weinberg provides a sufficiently detailed discussion of the symmetries inherent in a massive particle, including the little group that corresponds to those symmetries, his treatment of massless particles left me confused. Luckily I found a more detailed discussion of the symmetries of massless particles in the work of Y.S. Kim and coworkers. In addition to many journal articles on the subject, including many co-authored with Wigner himself, Kim and his colleague M.E. Noz have written two books which treat this topic: Theory and Applications of the Poincaré Group (Fundamental Theories of Physics) ; Phase Space Picture of Quantum Mechanics: Group Theoretical Approach (World Scientific Lecture Notes in Physics) . I have read the latter of these two books and have found it be extremely helpful! I should also note that there is a potential difficulty and source of confusion (as one other reviewer has already mentioned) due to Weinberg's choice of metric. Instead of g00=1; g11=g22=g33=-1, Weinberg goes with g00=-1; g11=g22=g33=1. Also, rather than describing a point in space-time as (t,x,y,z) like in most other QFT books, Weinberg orders the space-time coordinates as (x,y,z,t). Weinberg's conventions change the appearance of many of the equations, space-time matrices, and four vectors. As a result the Lorentz transformation matrices now look quite different. The dot product of the four vectors p and x changes sign using Weinberg's conventions, so that what would be exp(-p.r) in Ryder or Peskin and Schroeder becomes exp(+p.r) in Weinberg. Although I will eventually get used to Weinberg's conventions, I felt that I should post these observations as an alert to others who might consider dedicating themselves to the study of Weinberg.

### ⭐⭐⭐⭐⭐ QFT classic
*by J***E on February 19, 2026*

More than any other book on quantum field theory, Weinberg’s textbook has helped me feel that I almost understand what is really going on. The notation and conventions can be a little hard to work with.

### ⭐⭐⭐⭐⭐ Masterpiece
*by A***R on July 28, 2019*

I like the general philosophy behind the book. The author wants to explain why QFT is the way it is.

## Frequently Bought Together

- The Quantum Theory of Fields, Volume 1: Foundations
- General Relativity
- An Introduction To Quantum Field Theory

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*Last updated: 2026-05-19*