This is what POSIX 2003 says about ps:

By default, ps shall select  all processes with the same effective user
ID as the current user and the same controlling terminal as the invoker

ps [-aA][-defl][-G grouplist][-o format]...[-p proclist][-t termlist]
[-U userlist][-g grouplist][-n namelist][-u userlist]

-a     Write information for all processes associated  with  terminals.
       Implementations may omit session leaders from this list.

-A     Write information for all processes.

-d     Write information for all processes, except session leaders.

-e     Write information for all processes.  (Equivalent to -A.)

-f     Generate  a  full  listing. (See the STDOUT section for the con-
       tents of a full listing.)

-g  grouplist
       Write information for processes whose session leaders are  given
       in grouplist. The application shall ensure that the grouplist is
       a single argument in the form of a  <blank>  or  comma-separated
       list.

-G  grouplist
       Write  information for processes whose real group ID numbers are
       given in grouplist. The application shall ensure that the  grou-
       plist  is  a  single argument in the form of a <blank> or comma-
       separated list.

-l     Generate a long listing. (See STDOUT for the contents of a  long
       listing.)

-n  namelist
       Specify the name of an alternative system namelist file in place
       of the default. The name of the default file and the format of a
       namelist file are unspecified.

-o  format
       Write information according to the format specification given in
       format.  Multiple -o options can be specified; the format speci-
       fication shall be interpreted as the  <space>-separated concate-
       nation of all the format option-arguments.

-p  proclist
       Write  information  for  processes  whose process ID numbers are
       given in proclist. The application shall ensure  that  the  pro-
       clist  is  a  single argument in the form of a <blank> or comma-
       separated list.

-t  termlist
       Write information for processes associated with terminals  given
       in termlist. The application shall ensure that the termlist is a
       single argument in the form  of  a  <blank>  or  comma-separated
       list.  Terminal identifiers shall be given in an implementation-
       defined format.    On  XSI-conformant  systems,  they  shall  be
       given  in  one of two forms: the device's filename (for example,
       tty04) or, if the device's filename starts with  tty,  just  the
       identifier following the characters tty (for example, "04" ).

-u  userlist
       Write  information  for processes whose user ID numbers or login
       names are given in userlist. The application shall  ensure  that
       the  userlist  is  a single argument in the form of a <blank> or
       comma-separated list. In the  listing,  the  numerical  user  ID
       shall be written unless the -f option is used, in which case the
       login name shall be written.

-U  userlist
       Write information for processes whose real user  ID  numbers  or
       login  names are given in userlist. The application shall ensure
       that the userlist is a single argument in the form of a  <blank>
       or comma-separated list.

With  the  exception of -o format, all of the options shown are used to
select processes. If any are  specified,  the  default  list  shall  be
ignored  and ps shall select the processes represented by the inclusive
OR of all the selection-criteria options.

The  -o option allows the output format to be specified under user con-
trol.

The application shall ensure that the format specification is a list of
names  presented as a single argument, <blank> or comma-separated. Each
variable has a default header. The default header can be overridden  by
appending  an  equals  sign and the new text of the header. The rest of
the characters in the argument shall be used as the  header  text.  The
fields specified shall be written in the order specified on the command
line, and should be arranged in columns in the output. The field widths
shall  be  selected  by the system to be at least as wide as the header
text (default or overridden value). If the header text is null, such as
-o  user=,  the  field  width  shall be at least as wide as the default
header text. If all header text fields are null, no header  line  shall
be written.

ruser  The  real user ID of the process. This shall be the textual user
       ID, if it can be obtained and the field width permits, or a dec-
       imal representation otherwise.

user   The  effective user ID of the process. This shall be the textual
       user ID, if it can be obtained and the field width permits, or a
       decimal representation otherwise.

rgroup The  real  group  ID  of  the process. This shall be the textual
       group ID, if it can be obtained and the field width permits,  or
       a decimal representation otherwise.

group  The effective group ID of the process. This shall be the textual
       group ID, if it can be obtained and the field width permits,  or
       a decimal representation otherwise.

pid    The decimal value of the process ID.

ppid   The decimal value of the parent process ID.

pgid   The decimal value of the process group ID.

pcpu   The ratio of CPU time used recently to CPU time available in the
       same  period,  expressed  as  a  percentage.  The   meaning   of
       "recently"  in  this context is unspecified. The CPU time avail-
       able is determined in an unspecified manner.

vsz    The size of the process in (virtual) memory in 1024  byte  units
       as a decimal integer.

nice   The decimal value of the nice value of the process; see nice() .

etime  In the POSIX locale, the elapsed  time  since  the  process  was
       started, in the form: [[dd-]hh:]mm:ss

time   In the POSIX locale, the cumulative CPU time of the  process  in
       the form: [dd-]hh:mm:ss

tty    The name of the controlling terminal of the process (if any)  in
       the same format used by the who utility.

comm   The  name  of  the  command being executed ( argv[0] value) as a
       string.

args   The command with all its arguments as a string. The  implementa-
       tion may truncate this value to the field width; it is implemen-
       tation-defined whether any  further  truncation  occurs.  It  is
       unspecified  whether  the string represented is a version of the
       argument list as it was passed to the command when  it  started,
       or  is a version of the arguments as they may have been modified
       by the application. Applications cannot depend on being able  to
       modify  their  argument  list  and  having  that modification be
       reflected in the output of ps.

Any field need not be meaningful in all implementations. In such a case
a hyphen ( '-' ) should be output in place of the field value.

Only  comm  and  args  shall be allowed to contain <blank>s; all others
shall not.

The following table specifies the default header  to  be  used  in  the
POSIX locale corresponding to each format specifier.

    Format Specifier Default Header Format Specifier Default Header
    args             COMMAND        ppid             PPID
    comm             COMMAND        rgroup           RGROUP
    etime            ELAPSED        ruser            RUSER
    group            GROUP          time             TIME
    nice             NI             tty              TT
    pcpu             %CPU           user             USER
    pgid             PGID           vsz              VSZ
    pid              PID

There  is no special quoting mechanism for header text. The header text
is the rest of the argument. If multiple  header  changes  are  needed,
multiple -o options can be used, such as:

        ps -o "user=User Name" -o pid=Process\ ID