Return to Answer

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent (originally two-part, now turned into three-part) exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion - the three parts are listed below:

• J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban III. Convergence". arXiv:1304.0705 [math-ph]

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work. The third part of Dimock's exposé is meant to establish the convergence of the expansion scheme laid down in Parts I and II.

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent (originally two-part, now turned into three-part) exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion - the three parts are listed below:

• J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban III. Convergence". arXiv:1304.0705 [math-ph]

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work. The third part of Dimock's exposé is meant to establish the convergence of the expansion scheme laid down in Parts I and II.

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent (originally two-part, now turned into three-part) exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion - the first two parts are listed below:

• J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work. The upcoming third part of Dimock's exposé is meant to establish the convergence of the expansion scheme laid down in Parts I and II. Stay tuned...

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent (originally two-part, now turned into three-part) exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion - the three parts are listed below:

• J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban III. Convergence". arXiv:1304.0705 [math-ph]

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work. The third part of Dimock's exposé is meant to establish the convergence of the expansion scheme laid down in Parts I and II.

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent two-part exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion:

• J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work.

A small complement to Abdelmalek Abdesselam's answer: on the rigorous, non-perturbative side, there is also a recent (originally two-part, now turned into three-part) exposition by Jonathan Dimock, available in the arXiv's. He uses the $\phi^4$ scalar field theory in 3 dimensions in finite volume as a model for his discussion - the first two parts are listed below:

• J. Dimock, "The Renormalization Group According to Balaban I. Small Fields". arXiv:1108.1335 [math-ph]
• J. Dimock, "The Renormalization Group According to Balaban II. Large Fields". arXiv:1212.5562 [math-ph]

Tadeusz Balaban refined the method of block-spin renormalization group employed by Gallavotti, Kupiainen and many others for lattice field models in order to analyse "large field" regions, aiming at the treatment of the continuum limit of pure Yang-Mills models in finite volume and 4 dimensions. His long series of papers on the subject from the 80's remain essentially the state of the art towards the rigorous construction of realistic models in quantum field theory in 4 dimensions (see, for instance, the latest of the series), together with the paper of Magnen, Rivasseau and Sénéor, which was motivated by Balaban's work. The upcoming third part of Dimock's exposé is meant to establish the convergence of the expansion scheme laid down in Parts I and II. Stay tuned...