Elements of Physics, 50:750:131 Name _ Test 1 October 10, 2005
The working for all solutions must be shown. No credit will be given for an answer with no working. Take g to be 9.80 m/s2. 1. An astronomical unit (AU) is the average distance between Earth a
Little Note on Fierz
What is ( ) ( ) ?
If = , only 0 = and 3 = (1)+1 contribute, giving
1 (1)+ = 2 (1 ) = 2
for = .
If = , only 1 and 2 can contribute, in which case only = gives
nonzero, and then
1
either = , and the two terms cancel,
2
2
+
2
= 0,
1
Last Latexed: November 8, 2007 at 10:28
1
Schwinger trick and Feynman Parameters
Copyright c 2005 by Joel A. Shapiro
Here is the way Schwinger presented the method of combining propagators. An interesting anecdote of physics history is that Schwinger rema
Stress-Energy tensor for Maxwell Theory
Joel A. Shapiro
Maxwells theory of electromagnetism can be expressed in terms of a
4-vector eld A , coupled to a current j due to matter elds. The Lagrangian density given by
L = LMax + LMatter + LInt ,
where
1
and
Last Latexed: September 26, 2011 at 8:51
1
An extra note on Noethers Theorem
I was asked to clarify the connection of conserved charges emerging as a
consequence of a symmetry and the generator of those symmetry transformations.
Let us consider the simple
Faddeev-Popov ghosts
In evaluating the functional integral over gauge elds, we found that
we could add a gauge-xing term to the Lagrangian which would make the
integrals better dened and evaluatable in perturbation theory, but that in
order to do so, a ne
Some Comments on P&S treatment of BRST
Below 16.49
That Q2 vanishes on B and on c is trivial, the rst killed by the rst Q and
the second converted by the rst Q into a B and then killed by the second
Q. For the fermion eld
Q2 = Q(igca ta ) = igQ(ca )ta igc
Generating Functions for Diagrams
Joel Shapiro
April, 2002
The partition function and the energy functional
Before we continue with the computation of the eective action, lets review
the meanings of the generating functions we have already met. For simpli
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The beta function B (x, y )
Joel Shapiro
The Beta function is dened, for Re > 0, Re > 0, as
1
B (, ) =
0
dx x1 (1 x) 1 .
To evaluate this, consider
( + )B (, ) =
=
=
=
=
0
0
0
0
0
1
t+ 1 et dt
t
t 1 et dt
et dt
t
0
dx x1 (1 x) 1
u
du u1(1 ) 1
t
du u1(t u)
Last Latexed: January 26, 2010 at 11:21
1
Notes on Bessel Functions
Joel A. Shapiro, based on Arfken 3rd Edition
Bessel functions Jm (x) of integral order m may be dened by the generating function g (x, t) := e(x/2)(t 1/t) =
n=
Jn (x)tn
(1)
As the genera
CHAPTER 3 KINEMATICS IN TWO DIMENSIONS
CONCEPTUAL QUESTIONS
_
1.
REASONING AND SOLUTION In addition to the x and y axes, the z axis would be required to completely describe motion in three dimensions. Motion along the z axis can be described in terms of t
CHAPTER 4 FORCES AND NEWTON'S LAWS
OF MOTION
CONCEPTUAL QUESTIONS
_
1.
REASONING AND SOLUTION When the car comes to a sudden halt, the upper part of the body continues forward (as predicted by Newton's first law) if the force exerted by the lower back mus
GENERAL PHYSICS I
COURSE: 21:750:203:B1 General Physics I Summer 2008
CLASS MEETS: M, T, W,TH Instructor: Office: Telephone: Dr. John Rollino 357 Smith Hall 353-1573 (office) 10:15AM 12:30 in Smith 220
e-mail: jrollino@andromeda.rutgers.edu
Textbook: Cutn
PHY 205 Summer 2008
LAB SCHEDULE Lab Text: M Memorial Day Observed. University closed. 6/2 Geiger counter data presentation II 6/9 Motion II J. Rollino. Laboratory Notes for Introductory Physics. T 5/27 Labs do not meet. Students should obtain lab manual
Physics 235 Chapter 8 Central-Force Motion
Chapter 8
In this Chapter we will use the theory we have discussed in Chapter 6 and 7 and apply it to very important problems in physics, in which we study the motion of two-body systems on which central force ar
Physics 235 Chapter 9 Dynamics of a System of Particles
Chapter 09
In this Chapter we expand our discussion from the two-body systems discussed in Chapter 8 to systems that consist out of many particles. In general, these particles are exposed to both ext
Lightning review of groups
Copyright c 2005 by Joel A. Shapiro
We are going to be very concerned with symmetries of our theories, and symmetries form a group. I want to give a lightning review of what we need from Group Theory, though I suspect you will w
General Physics
I.
Introduction to Physics- The goal of physics is to gain a deeper
understanding of the world in which we live
a. Physics and the laws of naturei. Physics- study of the fundamental laws of nature, which, simply
put, are the laws that unde