European Mathematical Society - rodolfo gambini
https://euro-math-soc.eu/author/rodolfo-gambini
enA first course in Loop Quantum Gravity
https://euro-math-soc.eu/review/first-course-loop-quantum-gravity
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>As it is said in the preface of the book, Loop quantum gravity has emerged<br />
as a possible avenue towards the quantization of general relativity. This is<br />
one of the main streams to attack this outstanding problem in mathematical physics,<br />
although one has to recognize that it has had less impact than string and superstring<br />
theories.</p>
<p>Before starting to read the book, I was delighted to have in my hands what<br />
it seemed to be a leisurely introduction to a topic of such novelty, in<br />
which my background as differential geometer and (mathematical) gauge<br />
theorist could be well suited. The first chapters give overall<br />
introductions in differential geometry, general relativity, semi-riemannian<br />
geometry, always keeping an informal style. So informal that at some points<br />
in touches the incorrectness. However, when reading these chapters, some of<br />
the times even skipping parts (so basic for a mathematician), this was<br />
to be forgiven. Around the second third of the book, physical<br />
(and more interesting) ideas enter the discussion (Yang-Mills theories, quantum mechanics,<br />
quantum field theory), and then the book swaps to the usual "physics<br />
jargon", so extraneous to a mathematician. No much<br />
intention not to lose people not already familiar with the theory<br />
is shown in the text, accompanied by a lack of motivation when introducing physical concepts.<br />
Moreover, not even for the experts the material is<br />
going to be of much use, since details are skipped once and again. The third<br />
part of the book (loop general relativity, loop quantum cosmology) is basically<br />
a review of very technical material. This is where the book touches the topic<br />
announced in the title, but by then all arguments follow a physics line of<br />
reasoning: no rigorous proofs, renormalizations, divergences, etc.<br />
Again, I have gone through a text in mathematical<br />
physics on which my expectations have not been fulfilled. Maybe next time.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Vicente MuĂ±oz</div></div></div><div class="field field-name-field-review-legacy-affiliation field-type-text field-label-inline clearfix"><div class="field-label">Affiliation: </div><div class="field-items"><div class="field-item even">UCM</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>Loop quantum gravity has emerged as a possible avenue towards the<br />
quantization of general relativity. This book is an introduction to this<br />
topic, which is at the level of a graduate student in Theoretical Physics.<br />
The book covers: general relativity, hamiltonian mechanics, Yang-Mills<br />
theories, quantum mechanics, quantum field theories and loop quantum<br />
gravity.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/rodolfo-gambini" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">rodolfo gambini</a></li><li class="vocabulary-links field-item odd"><a href="/author/jorge-pullin" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">jorge pullin</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/oxford-university-press" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">oxford university press</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2011</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-0-19-959075-9</div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/81-quantum-theory" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">81 Quantum theory</a></li></ul></span>Tue, 19 Jun 2012 09:46:14 +0000Anonymous45452 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/first-course-loop-quantum-gravity#comments