Thursday, March 6, 2008
Group Theory in Quantum Field Theory
Group theory is one of the most important tools in quantum field theory. In Quantum Field Theory Demystified, available on Amazon.com, it is discussed in two chapters. I have posted one of those chapters here.
Thursday, February 21, 2008
String Theory: T-duality
Once, it appeared that there were 5 different string theories. Then in the early-mid 1980's the first superstring revolution occured, and like Buddist monks physicists discovered that the 5 string theories were actually different aspects or descriptions of one underlying theory.
Mathematically, it was discovered that the different string theories were related by dualities. One of these dualities, T-duality, relates a string theory of a small compact dimension on a circle to a string theory of a large dimension. We discuss this in this sample chapter from String Theory Demystified.
Mathematically, it was discovered that the different string theories were related by dualities. One of these dualities, T-duality, relates a string theory of a small compact dimension on a circle to a string theory of a large dimension. We discuss this in this sample chapter from String Theory Demystified.
Wednesday, February 20, 2008
String Theory Demystified Sample Chapter
Here is a sample chapter from String Theory Demsytified. It introduces some aspects of superstring theory. Admittedly it will be chapter 7 in the book, so you would need to read the first 6 chapters to really understand whats going on.
The book will be available soon on Amazon.com. Click here for more info:
http://www.amazon.com/String-Theory-Demystified-David-McMahon/dp/0071498702/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1203551689&sr=8-1
The book will be available soon on Amazon.com. Click here for more info:
http://www.amazon.com/String-Theory-Demystified-David-McMahon/dp/0071498702/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1203551689&sr=8-1
Saturday, February 16, 2008
String Theory and D-Brane Dynamics
All of you budding string theorists out there might want to check out An Introduction to String Theory and D-Brane Dynamics by Richard Szabo. At about 140 pages, this is a compact book (sorry for the pun) that gives you a quick and dirty introduction to d-branes.
A basic picture of d-branes and the universe is that (leaving out time for the purposes of this discussion) we live in a three dimensional world that is embedded in a higher dimensional space. The world we live in is a brane while the remaining extra dimensions form the "bulk". The term brane is derived from membrane, think of a sheet of rubber, its a flat 2-D surface in our 3-D world. Add a dimension and you have a 3-D "brane" that sits in a higher dimensional space.
Apparently string theory tells us that the fields of the standard model are trapped on the brane (electromagnetism, i.e. light for example), but gravity can "leak off" the brane and is free to travel into the higher dimensional bulk. This is because of the boundary conditions on the strings that transmit the known forces, the string state representing the photon has its ends stuck on the brane, but the graviton is a closed string that can go where it wants to, so alot of them end up traveling into the bulk which we can't perceive directly with our senses or instruments. So gravity appears to be a much weaker force.
So to the book. I have to say that Szabo's book is one of the most clearly written physics texts I have come across. Its a five star book in my opinion. I am not sure how it would do as a first time exposure to string theory, I read it after having slogged through a lot of other books. But its a lot clearer and more to the point than all of them. Plus the small size makes it a nice way to tackle string theory and get the main ideas quickly.
The book does require some background in field theory, so you should know how to work with Lagrangians, the action, and getting the equations of motion for example. But its highly recommended for those with the requisite physics and math background.
A basic picture of d-branes and the universe is that (leaving out time for the purposes of this discussion) we live in a three dimensional world that is embedded in a higher dimensional space. The world we live in is a brane while the remaining extra dimensions form the "bulk". The term brane is derived from membrane, think of a sheet of rubber, its a flat 2-D surface in our 3-D world. Add a dimension and you have a 3-D "brane" that sits in a higher dimensional space.
Apparently string theory tells us that the fields of the standard model are trapped on the brane (electromagnetism, i.e. light for example), but gravity can "leak off" the brane and is free to travel into the higher dimensional bulk. This is because of the boundary conditions on the strings that transmit the known forces, the string state representing the photon has its ends stuck on the brane, but the graviton is a closed string that can go where it wants to, so alot of them end up traveling into the bulk which we can't perceive directly with our senses or instruments. So gravity appears to be a much weaker force.
So to the book. I have to say that Szabo's book is one of the most clearly written physics texts I have come across. Its a five star book in my opinion. I am not sure how it would do as a first time exposure to string theory, I read it after having slogged through a lot of other books. But its a lot clearer and more to the point than all of them. Plus the small size makes it a nice way to tackle string theory and get the main ideas quickly.
The book does require some background in field theory, so you should know how to work with Lagrangians, the action, and getting the equations of motion for example. But its highly recommended for those with the requisite physics and math background.
Thursday, February 14, 2008
String Theory in a Nutshell
Lately I've been studying every string theory book I can get my hands on. Unfortunately there are not very many available, so I was excited about the release of String Theory in a Nutshell written by Elias Kiritsis.
First I'll get to the bottom line. This is a well written book that should be on your bookshelf if you're interested in this topic. Its pretty clear, up-to-date, and thorough.
That being said, I have some mixed feelings about the book because it isn't what I expected. My perceptions came about from reading the first book in this series, Quantum Field Theory in a Nutshell by Anthony Zee. Zee's book is a masterpiece. Its written in a laid-back, conversational style, and it breaks topics down so well that some chapters are only a couple of pages long. I would describe Zee's book as a breakthrough in physics publishing, its a new kind of text that makes a difficult subject (QFT) far more accessible to a lot more people.
I expected String Theory in a Nutshell to be written in the same style. But it's not. The book by Kiritsis is good, but its what I would call a typical physics book with a standard presentation. Many results are simply stated with not as much explanation or derivation as they deserve in a book that I assume is aimed at a reader encountering string theory the very first time.
I've had to read other books alongside this one to follow the discussion. My conclusion is that this book is good once you've had some exposure somewhere else. I think a reader tackling the subject for the first time is going to find a lot lacking if they only read this book.
On the other hand, if you have had previous exposure, the book is a good read. It is advertised as concise-that it is. It also lives up to its advertised clear presentation. But its disappointing in that it was not written like the Zee quantum field theory book was.
First I'll get to the bottom line. This is a well written book that should be on your bookshelf if you're interested in this topic. Its pretty clear, up-to-date, and thorough.
That being said, I have some mixed feelings about the book because it isn't what I expected. My perceptions came about from reading the first book in this series, Quantum Field Theory in a Nutshell by Anthony Zee. Zee's book is a masterpiece. Its written in a laid-back, conversational style, and it breaks topics down so well that some chapters are only a couple of pages long. I would describe Zee's book as a breakthrough in physics publishing, its a new kind of text that makes a difficult subject (QFT) far more accessible to a lot more people.
I expected String Theory in a Nutshell to be written in the same style. But it's not. The book by Kiritsis is good, but its what I would call a typical physics book with a standard presentation. Many results are simply stated with not as much explanation or derivation as they deserve in a book that I assume is aimed at a reader encountering string theory the very first time.
I've had to read other books alongside this one to follow the discussion. My conclusion is that this book is good once you've had some exposure somewhere else. I think a reader tackling the subject for the first time is going to find a lot lacking if they only read this book.
On the other hand, if you have had previous exposure, the book is a good read. It is advertised as concise-that it is. It also lives up to its advertised clear presentation. But its disappointing in that it was not written like the Zee quantum field theory book was.
Tuesday, February 12, 2008
String Theory Book Review Part One
OK right now I am working on my own string theory book, String Theory Demystified. In order to get this book done I've had to bone up on string theory myself. This means I'm spending a lot of time reading papers, articles, and every single string theory book that's been published.
Given that I am currently wading through all these books, I thought I would offer my readers my own opinions of them. I will be publishing condensed versions of my thoughts on Amazon.com as I go along. Yes, I am writing a book which will be in competition with these folks, but I am trying to be as honest as I can.
The first book I'm going to talk about is the venerable STRING THEORY VOLUME ONE by Joseph Polchinski. I want to start off by saying that this book is very professionally written. Polchinski is obviously a guy who really knows what he is doing, and can teach and write besides do mathematical calculations.
My take on this book is that its written solely for advanced graduate students in particle physics. Presumably Polchinski assumes the reader has taken a quantum field theory course (perhaps from the amazing Sidney Coleman before he unfortunately prematurely passed away) using Weinberg or some other tome at a similar level. The fact is in this book there is no messing around.
In many ways, this book definitely accomplishes what it sets out to do-give graduate level students and professional physicists an advanced string theory book that can prepare them for research. This book is not one that is going to hold your hand. Nonetheless, it is very well written and has a clear and well organized exposition.
The notorious "path integral" is of course, a vital component when learning string theory at this level. It is something I am currently struggling with in the development of my own book. Do I include it or pretend like it doesn't exist (like Zweibach say)? My point of view is that on a basic level people are capable of a lot more than they imagine. So high standards should be set. If you're an advanced undergraduate in math or physics, the brutal truth is you CAN learn string theory at the level of Polchinski, even if you're physics instructors think you need to be sucking your thumb.
Why am I saying this? Let me go on a brief tangent and then I'll get back to my review of the book. I went to school at a supposedly no-name place-The University of New Mexico in Albuquerque. But while there I discovered a brilliant instructor. We were lucky enough to have Pedro Embid, a guy with a Ph.D. in math from U.C. Berkeley who had two (2) appointments to the Institute of Advanced Study at Princeton.
Pedro is a master at his craft, and knows mathematics like the back of his hand. When he teaches, he challenges you to get to this level even if in reality the expectation is not that you're going to make it to 100% where he is.
I bring this up because Pedro never wore kid gloves in any of the classes I took from him. Even as an undergradate, we would have tackled physics at the level of Polchinski if that had been the subject we were studying.
For some reason physics professors that I've encountered refuse to really challenge their students and don't think they're capable of this. That is why they don't teach say, general relativity for undergraduates or propose the drivel by Hartle as an example of what an undergraduate text in GR should look like. That is a load of crap if you ask me. If you're able to take linear algebra as a junior, then you are able to take what we call graduate level quantum mechanics too. So why not teach seniors quantum field theory and even string theory?
OK back to the book. Somehow Polchinski's book and the book I am trying to write fit into this morass of physics education.
What I find basically annoying is that nobody, even Polchinski, seems to have found a CLEAR and SIMPLE way to teach people what a path integral is and how to calculate them. I give Polchinski a B+ for his effort in the appendix, but come on people-can't we do better? I have yet to read a description of what a path integral is without 1) Getting a major headache and 2) being able to sit down and calculate them. I think Polchinski or someone else with an inclination to writing textbooks ought to just focus on that-write a small book on path integrals that finally makes this technique accessible to the majority of the human race. OK so where are you in your string theory program. Just staring out? This is not the book for you. I like Becker, Becker & Schwarz for "beginnners" (I am assuming you have a significant background in math & physics, but maybe you're not a star grad student at Princeton). I also liked the books by Kaku. Once you've gone through Becker et. al. you can tackle this one. I think just a basic understanding of quantum field theory is all you need, but the stumbling block is going to be the path integral. If you get path integrals, then this book will be a breeze. If you don't, then you're not going to know what the hell he is talking about.
Given that I am currently wading through all these books, I thought I would offer my readers my own opinions of them. I will be publishing condensed versions of my thoughts on Amazon.com as I go along. Yes, I am writing a book which will be in competition with these folks, but I am trying to be as honest as I can.
The first book I'm going to talk about is the venerable STRING THEORY VOLUME ONE by Joseph Polchinski. I want to start off by saying that this book is very professionally written. Polchinski is obviously a guy who really knows what he is doing, and can teach and write besides do mathematical calculations.
My take on this book is that its written solely for advanced graduate students in particle physics. Presumably Polchinski assumes the reader has taken a quantum field theory course (perhaps from the amazing Sidney Coleman before he unfortunately prematurely passed away) using Weinberg or some other tome at a similar level. The fact is in this book there is no messing around.
In many ways, this book definitely accomplishes what it sets out to do-give graduate level students and professional physicists an advanced string theory book that can prepare them for research. This book is not one that is going to hold your hand. Nonetheless, it is very well written and has a clear and well organized exposition.
The notorious "path integral" is of course, a vital component when learning string theory at this level. It is something I am currently struggling with in the development of my own book. Do I include it or pretend like it doesn't exist (like Zweibach say)? My point of view is that on a basic level people are capable of a lot more than they imagine. So high standards should be set. If you're an advanced undergraduate in math or physics, the brutal truth is you CAN learn string theory at the level of Polchinski, even if you're physics instructors think you need to be sucking your thumb.
Why am I saying this? Let me go on a brief tangent and then I'll get back to my review of the book. I went to school at a supposedly no-name place-The University of New Mexico in Albuquerque. But while there I discovered a brilliant instructor. We were lucky enough to have Pedro Embid, a guy with a Ph.D. in math from U.C. Berkeley who had two (2) appointments to the Institute of Advanced Study at Princeton.
Pedro is a master at his craft, and knows mathematics like the back of his hand. When he teaches, he challenges you to get to this level even if in reality the expectation is not that you're going to make it to 100% where he is.
I bring this up because Pedro never wore kid gloves in any of the classes I took from him. Even as an undergradate, we would have tackled physics at the level of Polchinski if that had been the subject we were studying.
For some reason physics professors that I've encountered refuse to really challenge their students and don't think they're capable of this. That is why they don't teach say, general relativity for undergraduates or propose the drivel by Hartle as an example of what an undergraduate text in GR should look like. That is a load of crap if you ask me. If you're able to take linear algebra as a junior, then you are able to take what we call graduate level quantum mechanics too. So why not teach seniors quantum field theory and even string theory?
OK back to the book. Somehow Polchinski's book and the book I am trying to write fit into this morass of physics education.
What I find basically annoying is that nobody, even Polchinski, seems to have found a CLEAR and SIMPLE way to teach people what a path integral is and how to calculate them. I give Polchinski a B+ for his effort in the appendix, but come on people-can't we do better? I have yet to read a description of what a path integral is without 1) Getting a major headache and 2) being able to sit down and calculate them. I think Polchinski or someone else with an inclination to writing textbooks ought to just focus on that-write a small book on path integrals that finally makes this technique accessible to the majority of the human race. OK so where are you in your string theory program. Just staring out? This is not the book for you. I like Becker, Becker & Schwarz for "beginnners" (I am assuming you have a significant background in math & physics, but maybe you're not a star grad student at Princeton). I also liked the books by Kaku. Once you've gone through Becker et. al. you can tackle this one. I think just a basic understanding of quantum field theory is all you need, but the stumbling block is going to be the path integral. If you get path integrals, then this book will be a breeze. If you don't, then you're not going to know what the hell he is talking about.
Monday, February 11, 2008
Quantum Field Theory Demystified: Lagrangian Dynamics
The Lagrangian is an important tool used throughout quantum field theory. You can get a leg up in your studies by learning or reviewing the basics of Lagrangian dynamics. This is covered in chapter 2 of Quantum Field Theory Demystified, which is available for download here.
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