Del aware St at e Uni vers i t y
Department of Applied Mathematics and Theoretical Physics
Dover, DE 19901
Introduction to Many

Body Dynamics
60

731

00,
3 cr.
Text:
A. M. Zagoskin, H. E. Stanley, J. W. Lynn:
Quantum Theory of Many

Body Systems
recommended:
R. D. Mattuck:
A Guide to Feynman Diagrams in the Many

Body Problem
H.
Bruus, K.
Flensberg:
Many

Body Q
uantum Theory in Condensed Matter Physics: An Introduction
The aim of the course is to introduce, develop and discuss various methods developed for the
study of many (10
19
–
10
23
) interacting particles. Typically, such particles are sufficiently close for
qu
antum effects to play a crucial role, too many for a straightforward extension of the single particle
theory, but still finitely many, preventing a transition into (continuous) field theory. The standard
approach is then to replace the intractable multitud
e of interacting real particles with a relatively small
number of
quasiparticles
—
the elementary response of the system to external perturbation.
Prerequisite:
Mathematical methods of Physics IV
(26

667), or equivalent (vector calculus, linear
algebra, tens
ors, real and complex analysis, multivariate calculus)
,
Classical Mechanics
(26

652),
Quantum Mechanics II
(26

676). A successful student is expected to gain a working knowledge of the
covered material, so as to be able to (1)
follow the applications in th
e literature, (2)
solve typical
problems in the field, and (3)
discuss adequately the term

paper subject.
Topical schedule
:
Basic Concepts
Introduction; Propagation function in a one

body quantum theory; Perturbation
theory for the propagator; Second quant
ization
Green’s Functions at Zero Temperature
Green’s function of the many

body system; Perturbation theory
More on Green’s Functions, Equilibrium and Otherwise, and Their Application
Analytic properties of equilibrium green’s functions; Matsubara formalis
m;
Linear response theory; Nonequilibrium Green’s functions; Quantum kinetic
equations; Electrical conductivity and quantum point contacts; Method of
tunneling Hamiltonian
Methods of the many

Body Superconductivity
Introduction; Instability of the normal s
tate; Pairing (BCS) Hamiltonian;
Green’s functions of a superconductor; Andreev reflection; Tunneling of single
electrons and Cooper pairs
C
URRICULUM
C
OURSE
R
EVIEW
:
Introduction to Many

Body Dynamics
1.
Course Title/Number:
Introduction to Many

Body Dynamics /
60

731

00
2.
Number of Credits:
3
3.
Curriculum Prog
ram Title:
Ph.D. in Applied Mathematics and Theoretical Physics
4.
Curriculum/Course is:
[ X ]
New
[
]
Revised
[
]
Required Course
[
X
]
Elective Course
5.
List Prerequisites:
26

667
(Mathematical methods of Physics IV)
, or equivalent (vector ca
lculus, linear algebra,
tensors, real and complex analysis, multivariate calculus)
26

652
(Classical Mechanics)
26

676
(Quantum Mechanics)
6.
List Courses Being Replaced or Changed:
This is a new course.
7. List Courses Being Deleted:
No courses are bein
g deleted.
8. Needs Statement:
This course is needed for students pursuing a Ph.D. in all areas of theoretical physics and
especially for those interested in microscopic (quantum) physics underlying the phenomenological
properties of bulk materials
—
typica
l of
macroscopic
objects in everyday life. The course also serves as
a bridge between the fundamental, microscopic physics and its collective, macroscopic manifestations,
with an outlook towards
emergent
phenomena that are not reducible in any simple fashi
on.
9. Catalog Description of the Course:
This course introduces, develops and discusses various methods developed for the study of the
collective phenomena
of many (10
19
–
10
23
) interacting particles: too close neglect quantum effects, too
many for straigh
tforward extensions of single particle theory, but too few for a transition into
(continuous) field theory.
10. List of Objectives of the Course:
(
1
)
To provide an introduction to the body knowledge and techniques of many

body quantum
dynamics. (
2
)
To see
how these techniques apply to the analysis of the microscopic physics behind the
C
URRICULUM
C
OURSE
R
EVIEW
:
Superstrings and Beyond
macroscopic phenomena in bulk materials. (
3
)
To learn how to identify those phenomena throughout
theoretical physics, which are best described using these methods. (
4
)
To dev
elop the problem

solving
skills associated with the application of these methods in theoretical physics, and learn how to extract
experimentally verifiable information from such application.
11. Course Outline:
See the “
Topical schedule
” section in the at
tached brief syllabus.
12. Show how the proposed course fits into the curriculum or course sequence:
This course is an elective within the curriculum of the Ph.D. program in theoretical physics, and
is indispensable for students focusing on the collective
quantum physics of bulk materials. For an
overview of pre

requisite dependences and the course’s relation to other courses proposed herein, please
see the attached “
Proposed Course Dependencies
” chart.
13. Are there comparable courses in other department
s?
No.
14. How will the students be affected by this course change?
This course provides the students an opportunity to increase their integration with the research
program of the Department of Applied Mathematics and Theoretical Physics, by understanding
the
mathematical underpinnings of the techniques that are used in contemporary theoretical physics. This
course will improve students’ professional competence, employability in technical fields and ability to
pass professional examinations; the term paper
requirement will foster improving expository skills.
Neither this course nor its prerequisites increase the total number of semester hours in this curriculum or
the number of credit hours required for graduation.
15. What effect will this new course have
on College resource?
None: this course will not require new or additional resources or staffing.
16. How will the course benefit the College?
This course studies materials comprised of many interactive particles: too many to be analyzed
by usual quantum
mechanics, yet too few to be approximated by a continuous field. To this end, one
introduces the concept of
pseudoparticles,
which capture the essence of
collective
behavior but are
simple enough for straightforward analysis. This
paradigm

shift
and its su
ccessful quantitative
C
URRICULUM
C
OURSE
R
EVIEW
:
Introduction to Many

Body Dynamics
application to otherwise intractable collective phenomena make this course also interesting to students
pursuing a Ph.D. degree in other scientific and even some non

science fields.
17. How will the change affect the program?
This co
urse will introduce students to the use of
pseudoparticles
as a quantitatively successful
method of capturing the essential
collective
behavior of many interacting particles. In addition, this
course provides a successful example of a paradigm

shift in ana
lysis of physical phenomena, and so also
in the overall philosophy and methodology of theoretical physics. This course will be one of the
electives specific to the Ph.D. program (concentration in theoretical physics) in this department.
18. Evaluation of
Student Performance:
Homework Assignments
40 %
Term

paper (take

home final)
60 %
Sample homework assignments, in

term and final examination question

sheets, work sheets,
course notes, review sheets and term papers will be accessible on

line.
Course Struct
ure: Three (3) 50

minute lectures per week.
References
1.
A. M. Zagoskin, H. E. Stanley, J. W. Lynn:
Quantum Theory of Many

Body Systems
(Springer

Verlag, 1998, ISBN = 0387983848)
2.
R. D. Mattuck:
A Guide to Feynman Diagrams in the Many

Body Problem
(Dover Pub.
, 1992;
ISBN = 0486670473)
3.
H.
Bruus, K.
Flensberg:
Many

Body Quantum Theory in Condensed Matter Physics: An
Introduction
(Oxford University Press, 2004; ISBN = 0198566336)
Submitted to Department of Applied Mathematics and Theoretical Physics
by: Tristan
Hubsch, on 27th of November, 2007.
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