For the standard model, and in particular for its representation-theoretic aspects (which are crucial), I would refer you to the excellent recent article by John Baez and John Huerta from the Bulletin of the American Mathematical Society which can be found here:
http://www.ams.org/journals/bull/2010-47-03/S0273-0979-10-01294-2/home.html
There are also references to other articles and books here that could lead you further.
If you are interested more generally in quantum field theory and its description for mathematicians (where differential geometry plays a big role, in addition to representation theory), then there is the infamous 2-volume "Quantum Field and Strings: A course for mathematicians" which is written by (mostly) mathematicians. It's not going to necessarily give you the correct physical insight, however. Here are the links:
Volume 1
Volume 2
Other good possibilities are Freed-Uhlenbeck's "Geometry of Quantum Field Theory" from the PCMI (Park City) series, or the gargantuan "Mirror Symmetry" from the Clay Math monographs.
A good place to start is in low dimensions and there a good introduction can be found in
J. Kock, 2003, Frobenius Algebras and 2-D Topological Quantum Field Theories, number 59 in London Mathematical Society Student Texts, Cambridge U.P., Cambridge.
There are also old notes of Quinn that take a very neat homotopy theoretic approach to some of the problems:
F. Quinn, 1995, Lectures on axiomatic topological quantum field theory, in D. Freed and K. Uhlenbeck, eds., Geometry and Quantum Field Theory, volume 1 of IAS/Park City Math- ematics Series, AMS/IAS,.
These do not really get near the physics but you seem to indicate that that is not the direction you want to go in.
I like the links with higher category theory. I realise that this is not everyone's `cup of tea' but it does have some useful insights. I wrote a set of notes for a workshop in Lisbon in 2011 which contain a lot that might be useful (or might not!). They are available at
http://ncatlab.org/nlab/files/HQFT-XMenagerie.pdf
My advice would be to raid the net getting this sort of resource (storing it on your hard disc rather than printing it all out!), then as you start working your way through some of the stuff you have found there will be explanations available ready at hand. Start with the main ideas and `back fill', i.e. don't try to learn everything you might need before you start. If when reading some source material an idea that you are not happy with comes up, search it out then, just enough to make progress beyond that point easy. (Of course this is how one progresses through lots of areas of maths so ....)
(Those notes of mine exist in several different forms and lengths, so in a longer version some idea may be more developed.... so ask!)
.... and don't forget the summaries in the n-Lab can be a very useful place to start a search.
(I had at the back of my mind just now a reference to a seminar that I had some notes on .... but no idea of the source. A little search found me:
http://ncatlab.org/nlab/show/UC+Riverside+Seminar+on+Cobordism+and+Topological+Field+Theories
... One other thing, there are lectures by Lurie on this stuff on YouTube:
https://www.youtube.com/watch?v=Bo8GNfN-Xn4
that are well worth watching.)
Best Answer
If you really know nothing about physics I suggest you begin with any text book on physics for undergrad. Easy to read, it will introduce the main usual suspects. After, you'll ask again :)
I am not sure that jumping from nothing to quantum mechanics, or even worse quantum fields theory, would be wise, like jumping from nothing in math to algebraic geometry or K-Theory.
After that, it depends of course at what level of mathematical physics you want to stop. I will illustrate this with some examples:
Question: What is the "mass" of an isolated dynamical system?
Math Answer: It is the class of cohomology of the action of the group of Galilee, measuring the lack of equivariance of the moment map, on a symplectic manifold representing the isolated dynamical system.
Another question: Why in general relativity $E = mc^2$?
Math Answer: Because the group of Poincaré has no cohomology
Another, other question: What is the theorem of decomposition of motions around the center of gravity?
Math Answer: Let $(M,\omega)$ be a symplectic manifold with an hamiltonian action of the group of Galilee, if the "mass" of the system is not zero (in the sense above) then $M$ is the symplectic product or $({\bf R}^6, {\rm can})$, representing the motions of the center of gravity, by another symplectic manifold $(M_0,\omega_0)$, representing the motions around the center of gravity. The group of Galillee acting naturally on $\bf R^6$ and $SO(3) \times {\bf R}$ on $M_0$.
Another, other, other question: What are the constants of motions?
Math Answer: Let $(M,\omega)$ be a pre-symplectic manifold with an hamiltonian action of a Lie group $G$, then the moment map is constant on the characteristics of $\omega$, that is the integral manifolds of the vector distribution $x \mapsto \ker(\omega_x)$.
These answers are the mathematical versions of physics classical constructions, but it would be very difficult to appreciate them if you have no pedestrian introduction of physics. You may enjoy also Aristotles' book "Physics", as a first dish, just for tasting the flavor of physics :)
After that, you will be able to appreciate also quantum mechanics, but this is another question.
Addendum
Just before entering in the modern world of physics I would suggest few basic lectures for the winter evenings, near the fireplace (I'm sorry I write them down in french because I read them in french).
• Platon, Timée, trad. Émile Chambry.
• Aristote, La Physique, Éd. J. Vrin.
• Maïmonide, Le Guide des Égarés, Éd. Maisonneuve & Larose. (the part about time as an accident of motion, accident of the thing. Very deep and modern thoughts).
• Giordano Bruno, Le Banquet des Cendres, Éd. L’éclat.
• Galileo Galilei, Dialogue sur les Deux Grands Systèmes du Monde, Éd. Points.
• Albert Einstein, La Relativité, Éd. Payot.
• Joseph-Louis Lagrange, Mécanique Analytique, Éd. Blanchard.
• Felix Klein, Le Programme d’Erlangen, Éd. Gauthier-Villars.
• Jean-Marie Souriau, Structure des Systèmes Dynamiques, Éd. Dunod.
• Victor Guillement & Shlomo Sternberg, Geometric Asymptotics, AMS Math Books
• François DeGandt Force and Geometry in Newton Principia.