Here's a list:
http://stackoverflow.com/questions/388242/the-definitive-c-book-guide-and-list
Is this your first programming language? Then please do not start with C++. Start with something like Python or Ruby -- it is far more accessible. You can move on to C++ at a later stage.
Great read and a good book. Lots of topics and a refreshing look on QFT. Highly recommend it.
One caveat: you cannot learn QFT from this book. It simply does not dive into any details of the calculations. It's great as a supplement, but keep in mind that no course on QFT will ever use this...
This massive book on QFT is a standard text nowadays and used at many universities. The book is extensive and very detailed. If you manage to follow the text and keep up with all the nitty-gritty details, then you are well underway into mastering QFT -- but this is quite a challenge. The book is...
Three books on R used in the context of finance and statistics are:
Cryer - Introductory Statistics with R
Chan - Time Series -- Applications to Finance with R and S-Plus
Zivot, Wang - Modelling Financial Time Series with S-Plus
And some mathematical background:
Brockwell, Davis -...
You have to be careful here. You're probably using a coherent-state basis, which is a basis corresponding to eigenvalues of the field operators. This basis is overcomplete, so you need a compensating factor for this. Look at for instance Altland and Simons.
The chiral boson in 2D was introduced e.g. by Floreanini and Jackiw (see here: http://prl.aps.org/abstract/PRL/v59/i17/p1873_1 ). In particular eq. 20 is the Lagrangian of the 2D chiral boson.
There is also a relativistic version I believe (or, at least, a more covoriant notation), which is I...
What area of finance are you interested in? One area frequently linked to more fancy math is that of financial derivatives, or more general the area of quantitative risks. Check out:
http://www.markjoshi.com/RecommendedBooks.html
More interested in a general exposé? Check out:
Buchanan -- An...
There's a two-volume book by Toda, Kubo + third author. First part is on equilibrium, second one on non-equilibrium statistical mechanics. Great graduate texts.
In Geophysics it's all about the data -- noise filtering, time series analysis, stuff like that. You do a lot of field work (from day trips to a whole month), but spent the majority of your remaining time processing this data. So expect a lot of data analysis, lots of programming and of course...
The next quantity you can define to characterize a function or data set would be something like "the average deviation from the average". The way you define it is as:
\frac{1}{b-a}\int_{a}^b f(x) (x - c) dx
where c is the average value of f(x), defined by your integral.
This expression is...
I'm looking for any kind of reference on a multivariable generalization of a (confluent) hypergeometric function.
In particular, Horns list is a list of 34 two-variable hypergeometric functions, 20 of which are confluent. Then one of these has the following series expansion:
\Phi_2(\beta...
I agree with the advice on David Tong's notes in conjunction with his lecture series.
I would advice against Peskin and Schroeder, because of its size. I also advice against Zee as a first read, because, well.. it doesn't really teach you much about the computational side. (sorry niklaus!)
The ground state is not unique. An example is the Landau level quantization generated by the Hamiltonian,
H = \frac{(p-eA)^2}{2m}
This can be written as H = (a^\dagger a + \frac{1}{2}) with a suitable definition of the operator a. So the energy spectrum is precisely that of the harmonic...
When the Hamiltonian is time-dependent, time translational invariance is absent. Since the symmetry is absent, the corresponding Noether charge is not a conserved quantity. Put differently: energy is not conserved in systems with a time-dependent Hamiltonian. This applies to both classical and...
What's your background? Did you do one or two courses in quantum mechanics?
If not, then there's probably not a lot of books out there that will serve your needs.
Long story short: start diving into CFT.
The approach taken in CFT is very different from what you will find in standard field theory books. CFT has such a rigid structure, that we can bypass a lot of the simplifications which are usually made in other field theories. So a lot of that...
This is just a reference book - they don't derive integrals at all. It's just a collection of integrals precisely for the reason that you do not need to derive it yourself.
In fact, a lot of the integrals you find in there are just copy/pasted from other sources, such as the books on integrals...
It is just the Hamiltonian multiplied by (t-t'), so it is what you think it is. Here, you don't have to be careful with the ordering of the operator and the time-dependence, because the Hamiltonian never operates on time. Time and the Hamiltonian always commute.
Also keep in mind that this...
What you state about the time evolution operator is indeed correct -- it needs to be replaced by the integral version you mentioned.
But what's more subtle is the type of correlator that is being evalued. P&S only treat the ground state-to-ground state amplitudes. That is, they assume the...
The techniques developed by Peskin and Schroeder only apply to time-independent interactions. Time-dependent interactions require a more careful treatment of the time evolution operators. This is really the realm of non-equilibrium quantum field theory. The formalism that is being used here is...
Because it is the path integral for a Majorana field. The third path integral you wrote down would apply to a Dirac field. The second has no meaning. The first (and Srednicki's one) is the one that applies to a Majorana field.
In a nutshell, a Majorana field is a more "basic" object than a...
The time evolution operator for Hamiltonians which are not constant in time is
U(t,t_0) = \mathcal{T}\exp\left(-\frac{i}{\hbar}\int_{t_0}^t dt' H(t')\right)
where \mathcal{T} is the time ordering symbol. This exponential is just a short-way of writing the following power series:
U(t,t_0) = 1...
I have not followed the whole threat, so forgive me for barging in here, but....
Are you claiming that non-perturbative approaches can only be carried out using a path integral approach? Because that statement is simply wrong.
Take for instance Conformal Field Theory in two dimensions...